234:(Sound Navigation and Ranging) use the sound waves that propagate under the water to detect objects on or under the water surface. Two types of sonar systems can be defined the active one and the passive one. In active sonar, the system emits pulses of sound and listens to the returns that will be used to estimate parameters. In the passive sonar, the system is essentially listening for the sounds made by the target objects. It is very important to note the difference between the radar system that uses radio waves and the sonar system that uses sound waves, the reason why the sonar uses the sound wave is because sound waves travel farther in the water than do radar and light waves. In passive sonar, the receiving array has the capability of detecting distant objects and their locations. Deformable array are usually used in sonar systems where the antenna is typically drawn under the water. In active sonar, the sonar system emits sound waves (acoustic energy) then listening and monitoring any existing echo (the reflected waves). The reflected sound waves can be used to estimate parameters, such as velocity, position and direction etc. Difficulties and limitations in sonar systems comparing to radar systems emerged from the fact that the propagation speed of sound waves under the water is slower than the radio waves. Another source of limitation is the high propagation losses and scattering. Despite all these limitations and difficulties, sonar system remains a reliable technique for range, distance, position and other parameters estimation for underwater applications.
292:
sources; external noises as well as acoustic couplings of loudspeaker signals overwhelm and attenuate the desired speech signal. In addition to these external sources, the strength of the desired signal is reduced due to the relatively distance between speaker and microphones. Array processing techniques have opened new opportunities in speech processing to attenuate noise and echo without degrading the quality of and affecting adversely the speech signal. In general array processing techniques can be used in speech processing to reduce the computing power (number of computations) and enhance the quality of the system (the performance). Representing the signal as a sum of sub-bands and adapting cancellation filters for the sub-band signals can reduce the demanded computation power and lead to a higher performance system. Relying on multiple input channels allows designing systems of higher quality comparing to systems that use single channel and solving problems such as source localization, tracking and separation, which cannot be achieved in case of using single channel.
258:(telecommunication) can be done by technological means through either electrical signals (wired communication) or electromagnetic waves (wireless communication). Antenna arrays have emerged as a support technology to increase the usage efficiency of spectral and enhance the accuracy of wireless communication systems by utilizing spatial dimension in addition to the classical time and frequency dimensions. Array processing and estimation techniques have been used in wireless communication. During the last decade these techniques were re-explored as ideal candidates to be the solution for numerous problems in wireless communication. In wireless communication, problems that affect quality and performance of the system may come from different sources. The multiuser –medium multiple access- and multipath -signal propagation over multiple scattering paths in wireless channels- communication model is one of the most widespread communication models in wireless communication (mobile communication).
2935:
more fully exploit the underlying data model, leading to so-called parametric array processing methods. The cost of using such methods to increase the efficiency is that the algorithms typically require a multidimensional search to find the estimates. The most common used model based approach in signal processing is the maximum likelihood (ML) technique. This method requires a statistical framework for the data generation process. When applying the ML technique to the array processing problem, two main methods have been considered depending on the signal data model assumption. According to the
Stochastic ML, the signals are modeled as Gaussian random processes. On the other hand, in the Deterministic ML the signals are considered as unknown, deterministic quantities that need to be estimated in conjunction with the direction of arrival.
301:
The high image quality facilitates quantitative analysis and comparison with images at other wavelengths. In general, astronomy arrays can be divided into two classes: the beamforming class and the correlation class. Beamforming is a signal processing techniques that produce summed array beams from a direction of interest – used basically in directional signal transmission or reception- the basic idea is to combine elements in a phased array such that some signals experience destructive inference and other experience constructive inference. Correlation arrays provide images over the entire single-element primary beam pattern, computed off-line from records of all the possible correlations between the antennas, pairwise.
4454:(DFT) it is possible to analyze signals in the time domain as well as in the spectral domain. The first approach is "XF" correlation because it first cross-correlates antennas (the "X" operation) using a time-domain "lag" convolution, and then computes the spectrum (the "F" operation) for each resulting baseline. The second approach "FX" takes advantage of the fact that convolution is equivalent to multiplication in Fourier domain. It first computes the spectrum for each individual antenna (the F operation), and then multiplies pairwise all antennas for each spectral channel (the X operation). A FX correlator has an advantage over a XF correlators in that the computational complexity is
36:
262:
1093:. In the former, one forms some spectrum-like function of the parameter(s) of interest. The locations of the highest (separated) peaks of the function in question are recorded as the DOA estimates. Parametric techniques, on the other hand, require a simultaneous search for all parameters of interest. The basic advantage of using the parametric approach comparing to the spectral based approach is the accuracy, albeit at the expense of an increased computational complexity.
1620:
provide a solution to an underlying estimation problem for a given observed process. A class of spatial spectral estimation techniques is based on the eigen-value decomposition of the spatial covariance matrix. The rationale behind this approach is that one wants to emphasize the choices for the steering vector a(θ) which correspond to signal directions. The method exploits the property that the directions of arrival determine the eigen structure of the matrix.
212:
is done under the assumption that the wavefield is generated by a finite number of signal sources (emitters), and contains information about signal parameters characterizing and describing the sources. There are many applications related to the above problem formulation, where the number of sources, their directions and locations should be specified. To motivate the reader, some of the most important applications related to array processing will be discussed.
195:
166:
and spatial parameters become more important. Array processing emerged in the last few decades as an active area and was centered on the ability of using and combining data from different sensors (antennas) in order to deal with specific estimation task (spatial and temporal processing). In addition to the information that can be extracted from the collected data the framework uses the advantage prior knowledge about the geometry of the
4929:
4442:
whereas the signal waveforms are deterministic (arbitrary) and unknown. According to the
Deterministic ML the signals are considered as unknown, deterministic quantities that need to be estimated in conjunction with the direction of arrival. This is a natural model for digital communication applications where the signals are far from being normal random variables, and where estimation of the signal is of equal interest.
6432:
238:
305:
5794:
1039:“The target is to estimate the DOA’s θ1, θ2, θ3, θ4 …θq of the sources from the M snapshot of the array x(t1)… x(tM). In other words what we are interested in is estimating the DOA’s of emitter signals impinging on receiving array, when given a finite data set {x(t)} observed over t=1, 2 … M. This will be done basically by using the second-order statistics of data”
6535:
processing will increase. It is highly expected that the importance of array processing will grow as the automation becomes more common in industrial environment and applications, further advances in digital signal processing and digital signal processing systems will also support the high computation requirements demanded by some of the estimation techniques.
2415:
5465:
6231:
2664:
5604:
228:
mode the antenna array based system radiates pulses and listens for the returns. By using the returns, the estimation of parameters such as velocity, range and DOAs (direction of arrival) of target of interest become possible. Using the passive far-field listening arrays, only the DOAs can be estimated.
2943:
The stochastic maximum likelihood method is obtained by modeling the signal waveforms as a
Gaussian random process under the assumption that the process x(t) is a stationary, zero-mean, Gaussian process that is completely described by its second-order covariance matrix. This model is a reasonable one
227:
used basically to detect objects by using radio waves. The range, altitude, speed and direction of objects can be specified. Radar systems started as military equipments then entered the civilian world. In radar applications, different modes can be used, one of these modes is the active mode. In this
202:
There are four assumptions in array processing. The first assumption is that there is uniform propagation in all directions of isotropic and non-dispersive medium. The second assumption is that for far field array processing, the radius of propagation is much greater than size of the array and that
334:
narrow band sources of known center frequency ω and locations θ1, θ2, θ3, θ4 ... θq. since the signals are narrow band the propagation delay across the array is much smaller than the reciprocal of the signal bandwidth and it follows that by using a complex envelop representation the array output can
317:
In addition to these applications, many applications have been developed based on array processing techniques: Acoustic
Beamforming for Hearing Aid Applications, Under-determined Blind Source Separation Using Acoustic Arrays, Digital 3D/4D Ultrasound Imaging Array, Smart Antennas, Synthetic aperture
300:
Astronomical environment contains a mix of external signals and noises that affect the quality of the desired signals. Most of the arrays processing applications in astronomy are related to image processing. The array used to achieve a higher quality that is not achievable by using a single channel.
269:
In the case of multiuser communication environment, the existence of multiuser increases the inter-user interference possibility that can affect quality and performance of the system adversely. In mobile communication systems the multipath problem is one of the basic problems that base stations have
245:
NORSAR is an independent geo-scientific research facility that was founded in Norway in 1968. NORSAR has been working with array processing ever since to measure seismic activity around the globe. They are currently working on an
International Monitoring System which will comprise 50 primary and 120
211:
The ultimate goal of sensor array signal processing is to estimate the values of parameters by using available temporal and spatial information, collected through sampling a wavefield with a set of antennas that have a precise geometry description. The processing of the captured data and information
165:
is an important and basic part of signal processing field, which used to deal with estimation problem in which the values of several parameters of the system should be estimated based on measured/empirical data that has a random component. As the number of applications increases, estimating temporal
6538:
In this article we emphasized the importance of array processing by listing the most important applications that include a form of array processing techniques. We briefly describe the different classifications of array processing, spectral and parametric based approaches. Some of the most important
282:
Array processing techniques got on much attention from medical and industrial applications. In medical applications, the medical image processing field was one of the basic fields that use array processing. Other medical applications that use array processing: diseases treatment, tracking waveforms
4441:
While the background and receiver noise in the assumed data model can be thought of as emanating from a large number of independent noise sources, the same is usually not the case for the emitter signals. It therefore appears natural to model the noise as a stationary
Gaussian white random process
1043:
In order to solve this problem (to guarantee that there is a valid solution) do we have to add conditions or assumptions on the operational environment and\or the used model? Since there are many parameters used to specify the system like the number of sources, the number of array elements ...etc.
6534:
Array processing technique represents a breakthrough in signal processing. Many applications and problems which are solvable using array processing techniques are introduced. In addition to these applications within the next few years the number of applications that include a form of array signal
2934:
While the spectral-based methods presented in the previous section are computationally attractive, they do not always yield sufficient accuracy. In particular, for the cases when we have highly correlated signals, the performance of spectral-based methods may be insufficient. An alternative is to
257:
can be defined as the process of exchanging of information between two or more parties. The last two decades witnessed a rapid growth of wireless communication systems. This success is a result of advances in communication theory and low power dissipation design process. In general, communication
1109:
The first method used to specify and automatically localize the signal sources using antenna arrays was the beamforming technique. The idea behind beamforming is very simple: steer the array in one direction at a time and measure the output power. The steering locations where we have the maximum
1619:
Many spectral methods in the past have called upon the spectral decomposition of a covariance matrix to carry out the analysis. A very important breakthrough came about when the eigen-structure of the covariance matrix was explicitly invoked, and its intrinsic properties were directly used to
291:
Speech enhancement and processing represents another field that has been affected by the new era of array processing. Most of the acoustic front end systems became fully automatic systems (e.g. telephones). However, the operational environment of these systems contains a mix of other acoustic
2925:
MUSIC spectrum approaches use a single realization of the stochastic process that is represent by the snapshots x (t), t=1, 2 ...M. MUSIC estimates are consistent and they converge to true source bearings as the number of snapshots grows to infinity. A basic drawback of MUSIC approach is its
2126:
6427:{\displaystyle {\tilde {\mathbf {R} }}\approx (\mathbf {I} -\alpha \mathbf {u} _{1}\mathbf {u} _{1}^{\dagger })\mathbf {R} (\mathbf {I} -\alpha \mathbf {u} _{1}\mathbf {u} _{1}^{\dagger })=\mathbf {R} -\mathbf {u} _{1}\mathbf {u} _{1}^{\dagger }\lambda _{1}(2\alpha -\alpha ^{2})}
5313:
5304:
1979:
3675:
5058:
5904:
220:
array processing concept was closely linked to radar and sonar systems which represent the classical applications of array processing. The antenna array is used in these systems to determine location(s) of source(s), cancel interference, suppress ground clutter.
4615:
2420:
2926:
sensitivity to model errors. A costly procedure of calibration is required in MUSIC and it is very sensitive to errors in the calibration procedure. The cost of calibration increases as the number of parameters that define the array manifold increases.
5789:{\displaystyle {\tilde {\mathbf {R} }}=(\sigma _{s}^{2}\mathbf {a} \mathbf {a} ^{\dagger }+\sigma _{n}^{2}\mathbf {I} )^{-{\frac {1}{2}}}\mathbf {R} (\sigma _{s}^{2}\mathbf {a} \mathbf {a} ^{\dagger }+\sigma _{n}^{2}\mathbf {I} )^{-{\frac {1}{2}}}}
6200:
4432:
2121:
1219:
4089:
1843:
3919:
3503:
3163:
1494:
1080:
Throughout this survey, it will be assumed that the number of underlying signals, q, in the observed process is considered known. There are, however, good and consistent techniques for estimating this value even if it is not known.
6012:
203:
there is plane wave propagation. The third assumption is that there is a zero mean white noise and signal, which shows uncorrelation. Finally, the last assumption is that there is no coupling and the calibration is perfect.
3278:
748:
4208:
2410:{\displaystyle \textstyle 3.\ Check\ which\ a(\theta )\ \epsilon span\{\mathbf {E} _{s}\}\ or\ \mathbf {P} _{A}a(\theta )\ or\ P_{\mathbf {A} }^{\perp }a(\theta ),\ where\ \mathbf {P} _{A}\ is\ a\ projection\ matrix.}
442:
6504:
2837:
4785:
182:
communications. One of the main advantages of using array processing along with an array of sensors is a smaller foot-print. The problems associated with array processing include the number of sources used, their
1335:
6809:
Zelinski, Rainer. "A microphone array with adaptive post-filtering for noise reduction in reverberant rooms." Acoustics, Speech, and Signal
Processing, 1988. ICASSP-88., 1988 International Conference on. IEEE,
6075:
5460:{\displaystyle {\tilde {\mathbf {R} }}=\mathbf {P} _{a}^{\perp }\mathbf {R} \mathbf {P} _{a}^{\perp }=\mathbf {P} _{a}^{\perp }\mathbf {R} _{v}\mathbf {P} _{a}^{\perp }+\sigma _{n}^{2}\mathbf {P} _{a}^{\perp }}
1595:
270:
to deal with. Base stations have been using spatial diversity for combating fading due to the severe multipath. Base stations use an antenna array of several elements to achieve higher selectivity, so called
3787:
693:
160:
Array processing metrics are often assessed noisy environments. The model for noise may be either one of spatially incoherent noise, or one with interfering signals following the same propagation physics.
5214:
3378:
1848:
3038:
4289:
3508:
2741:
4968:
5803:
1626:
algorithm. MUSIC was originally presented as a DOA estimator, then it has been successfully brought back to the spectral analysis/system identification problem with its later development.
2659:{\displaystyle \textstyle 4.\ Search\ for\ all\ possible\ \theta \ such\ that:\left|P_{\mathbf {A} }^{\perp }a(\theta )\right|^{2}=0\ or\ M(\theta )={\frac {1}{P_{A}a(\theta )}}=\infty }
5523:
5207:
4509:
7095:
S. Haykin and K.J.R. Liu (Editors), "Handbook on Array
Processing and Sensor Networks", Adaptive and Learning Systems for Signal Processing, Communications, and Control Series, 2010.
246:
auxiliary seismic stations around the world. NORSAR has ongoing work to improve array processing to improve monitoring of seismic activity not only in Norway but around the globe.
4879:
4667:
3959:
127:. Wave propagation means there is a systemic relationship between the signal received on spatially separated sensors. By creating a physical model of the wave propagation, or in
7102:
5965:
5089:
4915:
4499:
5153:
5121:
4120:
6131:
552:
4294:
1030:
937:
844:
6224:
6124:
6102:
5936:
5597:
5567:
5545:
5489:
4961:
1984:
1120:
579:
3964:
1637:
5173:
4837:
3792:
514:
6524:
1611:. The advantages of using beamforming technique are the simplicity, easy to use and understand. While the disadvantage of using this technique is the low resolution.
2921:
4687:
613:
476:
3383:
3043:
6881:
1340:
283:
that have information about the condition of internal organs e.g. the heart, localizing and analyzing brain activity by using bio-magnetic sensor arrays.
5970:
3168:
99:
that extends from the simplest form of 1 dimensional line arrays to 2 and 3 dimensional array geometries. Array structure can be defined as a set of
4450:
The problem of computing pairwise correlation as a function of frequency can be solved by two mathematically equivalent but distinct ways. By using
701:
4125:
339:
6982:
Amir Leshem; Albert-Jan
Boonstra; Alle-Jan van der Veen (November 2000). "Multichannel Interference Mitigation Techniques in Radio Astronomy".
6760:
6439:
2746:
330:
arbitrary sensors that have arbitrary locations and arbitrary directions (directional characteristics) which receive signals that generated by
4697:
1224:
6605:
5908:
This approach requires much more computationally intensive matrix manipulations, and again the visibilities covariance matrix is altered.
7128:
6017:
1499:
6824:(September 12, 2008). "A Scalable Correlator Architecture Based on Modular FPGA Hardware, Reuseable Gateware, and Data Packetization".
7058:
3680:
5299:{\displaystyle \mathbf {P} _{a}^{\perp }=\mathbf {I} -\mathbf {a} (\mathbf {a} ^{\dagger }\mathbf {a} )^{-1}\mathbf {a} ^{\dagger }}
1974:{\displaystyle \textstyle R_{x}=\mathbf {A} \mathbf {R} _{s}\mathbf {A} ^{*}+\sigma ^{2}I=\sum _{k=1}^{M}\lambda _{k}e_{k}r_{k}^{*}}
623:
4963:
that is not a known function of the direction of interference and its time variance, the signal covariance matrix takes the form:
6937:
Amir Leshem; Alle-Jan van der Veen (August 16, 2000). "Radio astronomical imaging in the presence of strong radio interference".
3283:
4925:
In radio astronomy, RF interference must be mitigated to detect and observe any meaningful objects and events in the night sky.
3670:{\displaystyle \textstyle =min_{a^{*}(\theta _{k}w_{k}=1)}\ W_{k}^{*}R_{k}W_{k}+2\mu (a^{*}(\theta _{k})w_{k}\Leftrightarrow 1)}
2954:
5569:. The disadvantages to this approach include altering the visibilities covariance matrix and coloring the white noise term.
5053:{\displaystyle \mathbf {R} =\mathbf {R} _{v}+\sigma _{s}^{2}\mathbf {a} \mathbf {a} ^{\dagger }+\sigma _{n}^{2}\mathbf {I} }
274:. Receiving array can be directed in the direction of one user at a time, while avoiding the interference from other users.
2669:
135:
set, the relationships between the signals received on spatially separated sensors can be leveraged for many applications.
1101:
Spectral based algorithmic solutions can be further classified into beamforming techniques and subspace-based techniques.
5899:{\displaystyle {\tilde {\mathbf {R} }}=(\cdot )^{-{\frac {1}{2}}}\mathbf {R} _{v}(\cdot )^{-{\frac {1}{2}}}+\mathbf {I} }
5547:, in particular the matrix containing an orthonormal basis of the noise subspace, which is the orthogonal complement of
4213:
7110:
N. Petrochilos, G. Galati, E. Piracci, Array processing of SSR signals in the multilateration context, a decade survey.
6526:. This scheme requires an accurate estimation of the interference term, but does not alter the noise or sources term.
7098:
E. Tuncer and B. Friedlander (Editors), "Classical and Modern
Direction-of-Arrival Estimation", Academic Press, 2010.
4803:
Cross-correlation spectroscopy with spatial interferometry, is possible by simply substituting a signal with voltage
79:
57:
5577:
This scheme attempts to make the interference-plus-noise term spectrally white. To do this, left and right multiply
5209:, which, when left and right multiplied by the signal covariance matrix, will reduce the interference term to zero.
50:
6876:
6734:
6539:
algorithms are covered, the advantage(s) and the disadvantage(s) of these algorithms also explained and discussed.
1110:
power yield the DOA estimates. The array response is steered by forming a linear combination of the sensor outputs.
4610:{\displaystyle S_{\text{XX}}(f)=\int _{-\infty }^{\infty }R_{\text{XX}}(\tau )\cos(2\pi f\tau ),\mathrm {d} \tau }
584:τi(θk): is the propagation delay between the first and the ith sensor for a waveform coming from direction (θk),
6553:
5494:
5178:
1044:
are there conditions that should be met first? Toward this goal we want to make the following assumptions:
4848:
4636:
3924:
697:
If we assume now that M snapshots are taken at time instants t1, t2 ... tM, the data can be expressed as:
6899:
6195:{\displaystyle {\tilde {\mathbf {R} }}=\mathbf {R} -\sigma _{s}^{2}\mathbf {a} \mathbf {a} ^{\dagger }}
4451:
5941:
5065:
4884:
4468:
4427:{\displaystyle \textstyle W_{k}=R_{x}^{-1}a(\theta _{k})/(a^{*}(\theta _{k})R_{x}^{-1}a(\theta _{k}))}
5126:
5094:
4094:
6764:
2116:{\displaystyle \textstyle 2.\ span\{\mathbf {A} \}=spane\{e1,....,e_{d}\}=span\{\mathbf {E} _{s}\}.}
1214:{\displaystyle \textstyle 1.\ R_{x}={\frac {1}{M}}\sum _{t=1}^{M}\mathbf {x} (t)\mathbf {x} ^{*}(t)}
521:
4462:
4084:{\displaystyle \textstyle a^{*}(\theta _{k})W_{k}=\mu a(\theta _{k})^{*}R_{x}^{-1}a(\theta _{k})=1}
942:
849:
756:
44:
6207:
6107:
6080:
5919:
5798:
The calculation requires rigorous matrix manipulations, but results in an expression of the form:
5580:
5550:
5528:
5472:
4944:
1838:{\displaystyle \textstyle 1.\ Subspace\ decomposition\ by\ performing\ eigenvalue\ decomposition:}
4465:
vary the time lag between signals obtain the power spectrum of input signals. The power spectrum
3914:{\displaystyle \textstyle R_{x}w_{k}=\mu a(\theta _{k}),\ or\ W_{k}=\mu R_{x}^{-1}a(\theta _{k})}
557:
2944:
if the measurements are obtained by filtering wide-band signals using a narrow band-pass filter.
1622:
The tremendous interest in the subspace based methods is mainly due to the introduction of the
61:
5158:
4806:
483:
6509:
146:
2846:
7001:
6911:
6843:
6573:
4672:
3498:{\displaystyle \textstyle min_{a^{*}(\theta _{k}w_{k}=1)}\ E\{\left|W_{k}X(t)\right|^{2}\}}
3158:{\displaystyle \textstyle min_{a^{*}(\theta _{k}w_{k}=1)}\ E\{\left|W_{k}X(t)\right|^{2}\}}
1607:. Different beamforming approaches correspond to different choices of the weighting vector
516:
is the signal emitted by the kth source as received at the frequency sensor 1 of the array,
254:
184:
24:
7077:
589:
452:
123:. However, many similarities exist, the most fundamental of which may be an assumption of
8:
7005:
6915:
6847:
7017:
6991:
6964:
6946:
6859:
6833:
2841:
1489:{\displaystyle \textstyle 3.\ Find\ Peaks\ of\ B(W_{i})\ for\ all\ possible\ w_{i}'s.}
6568:
1623:
1604:
162:
96:
7021:
6863:
4941:
For an array of Radio Telescopes with a spatial signature of the interfering source
7123:
7069:
7009:
6981:
6968:
6956:
6919:
6851:
6578:
6007:{\displaystyle \mathbf {R} =\mathbf {U} \mathbf {\Lambda } \mathbf {U} ^{\dagger }}
128:
124:
6897:
6885:
104:
20:
3273:{\displaystyle \textstyle =min_{a^{*}(\theta _{k}w_{k}=1)}\ W_{k}^{*}R_{k}W_{k}}
6821:
6563:
4501:
of a signal is related to its autocorrelation function by a Fourier transform:
4455:
7117:
132:
116:
108:
6126:. One can subtract the interference term from the signal covariance matrix:
4932:
An array of radio telescopes with an incoming radio wave and RF interference
1058:
Isotropic and non-dispersive medium – Uniform propagation in all directions.
6685:
6656:
6619:
6548:
743:{\displaystyle \mathbf {X} =\mathbf {A} (\theta )\mathbf {S} +\mathbf {N} }
261:
167:
7107:
Prof. J.W.R. Griffiths, Adaptive array processing, IEEPROC, Vol. 130,1983.
4203:{\displaystyle \textstyle \mu =a(\theta _{k})^{*}R_{x}^{-1}a(\theta _{k})}
1048:
The number of signals is known and is smaller than the number of sensors,
437:{\displaystyle \textstyle x(t)=\sum _{K=1}^{q}a(\theta _{k})s_{k}(t)+n(t)}
138:
Some common problem that are solved with array processing techniques are:
6996:
6951:
6660:
6558:
6499:{\displaystyle \lambda _{1}(2\alpha -\alpha ^{2})\approx \sigma _{s}^{2}}
2832:{\displaystyle \textstyle P_{A}^{\perp }=I-E_{s}E_{s}^{*}=E_{n}E_{n}^{*}}
271:
6898:
Jamil Raza; Albert-Jan Boonstra; Alle-Jan van der Veen (February 2002).
6738:
4780:{\displaystyle R_{\text{XX}}(\tau )=\left(V_{X}(t)V_{X}(t+\tau )\right)}
5599:
with inverse square root factors of the interference-plus-noise terms.
5175:
denotes the Hermitian transpose. One can construct a projection matrix
194:
112:
111:. The sensors used for a specific problem may vary widely, for example
7073:
6960:
6923:
318:
radar, underwater acoustic imaging, and Chemical sensor arrays...etc.
6608:. Signal and Image Processing Seminar. University of Texas at Austin.
4458:(N). Therefore, FX correlators are more efficient for larger arrays.
1330:{\displaystyle \textstyle 2.\ Calculate\ B(W_{i})=F^{*}R_{x}F(W_{i})}
1089:
In general, parameters estimation techniques can be classified into:
188:
120:
7013:
6855:
6070:{\displaystyle \sigma _{s}^{2}\approx \lambda _{1}-\sigma _{n}^{2}}
304:
179:
6838:
4928:
1590:{\displaystyle \textstyle 4.\ Calculate\ \theta _{k},\ i=1,....q.}
265:
Multi-path communication problem in wireless communication systems
6936:
3782:{\displaystyle \textstyle 3.\ Differentiating\ it,\ we\ obtain}
619:
The same equation can be also expressed in the form of vectors:
237:
100:
6014:, and likewise the best estimate of the interference power is
688:{\displaystyle \textstyle \mathbf {x} (t)=A(\theta )s(t)+n(t)}
230:
223:
175:
171:
170:
to perform the estimation task. Array processing is used in
3373:{\displaystyle \textstyle 2.\ Use\ the\ langrange\ method:}
478:
is the vector of the signals received by the array sensors,
150:
5938:
is unknown, the best estimate is the dominant eigenvector
1055:
The set of any q steering vectors is linearly independent.
142:
determine number and locations of energy-radiating sources
6900:"Spatial Filtering of RF Interference in Radio Astronomy"
3033:{\displaystyle \textstyle 1.\ Find\ W_{K}\ to\ minimize:}
321:
6826:
Publications of the Astronomical Society of the Pacific
5911:
335:
be expressed (by the sense of superposition) as :
4298:
4217:
4129:
4098:
3968:
3928:
3796:
3684:
3512:
3387:
3287:
3172:
3047:
2958:
2750:
2673:
2424:
2130:
1988:
1852:
1641:
1503:
1344:
1228:
1124:
627:
554:
is the steering vector of the array toward direction (
343:
6512:
6442:
6234:
6210:
6134:
6110:
6083:
6020:
5973:
5944:
5922:
5806:
5607:
5583:
5553:
5531:
5497:
5475:
5316:
5217:
5181:
5161:
5129:
5097:
5068:
4971:
4947:
4887:
4851:
4809:
4700:
4675:
4639:
4512:
4471:
4297:
4216:
4128:
4097:
3967:
3927:
3795:
3683:
3511:
3386:
3286:
3171:
3046:
2957:
2849:
2749:
2736:{\displaystyle \textstyle 5.\ After\ EVD\ of\ R_{x}:}
2672:
2423:
2129:
1987:
1851:
1640:
1502:
1343:
1227:
1123:
945:
852:
759:
704:
626:
592:
560:
524:
486:
455:
342:
6819:
5525:
can be constructed using the eigen-decomposition of
752:
Where X and N are the r × M matrices and S is q × M:
6518:
6498:
6426:
6218:
6194:
6118:
6096:
6069:
6006:
5959:
5930:
5898:
5788:
5591:
5561:
5539:
5517:
5483:
5459:
5308:So the modified signal covariance matrix becomes:
5298:
5201:
5167:
5147:
5115:
5083:
5052:
4955:
4909:
4873:
4831:
4779:
4681:
4661:
4609:
4493:
4426:
4284:{\displaystyle \textstyle 5.\ Capon's\ Beamformer}
4283:
4202:
4114:
4083:
3953:
3913:
3781:
3669:
3497:
3372:
3272:
3157:
3032:
2915:
2831:
2735:
2658:
2409:
2115:
1973:
1837:
1589:
1488:
1329:
1213:
1024:
931:
838:
742:
687:
607:
573:
546:
508:
470:
436:
7059:"Two Decades of Array Signal Processing Research"
6798:Sensor Array Signal Processing: Two Decades Later
5091:is the visibilities covariance matrix (sources),
7115:
4936:
1071:a. Radius of propagation >> size of array.
1061:Zero mean white noise and signal, uncorrelated.
7038:
151:signal-to-interference-plus-noise ratio (SINR)
4920:
2929:
6655:
4436:
3491:
3449:
3151:
3109:
2218:
2203:
2106:
2091:
2073:
2036:
2015:
2007:
326:Consider a system that consists of array of
4445:
1614:
1096:
1091:spectral based and parametric based methods
95:is a wide area of research in the field of
7056:
6795:
296:Array Processing in Astronomy Applications
7047:
6995:
6950:
6837:
6600:
6598:
6596:
6594:
5518:{\displaystyle \mathbf {P} _{a}^{\perp }}
5202:{\displaystyle \mathbf {P} _{a}^{\perp }}
4669:for signal X as a function of time delay
2938:
80:Learn how and when to remove this message
6719:
4927:
1104:
1084:
308:One antenna of the Allen Telescope Array
303:
260:
236:
193:
178:, seismic exploration, anti-jamming and
43:This article includes a list of general
7039:Johnson, D. H.; Dudgeon, D. E. (1993).
6984:Astrophysical Journal Supplement Series
6939:IEEE Transactions on Information Theory
287:Array Processing for Speech Enhancement
7116:
6878:Spectrometers for Heterodyne Detection
6870:
6791:
6789:
6787:
6785:
6783:
6781:
6720:Singh, Hema; Jha, RakeshMohan (2012),
6715:
6713:
6711:
6709:
6707:
6705:
6703:
6701:
6699:
6679:
6677:
6675:
6651:
6649:
6647:
6645:
6643:
6641:
6639:
6637:
6635:
6633:
6591:
1624:MUSIC (Multiple Signal Classification)
6727:
322:General model and problem formulation
16:Area of research in signal processing
6683:
6617:
5912:Subtraction of interference estimate
5572:
5123:is the power of the interferer, and
4874:{\displaystyle R_{\text{XY}}(\tau )}
4691:
4662:{\displaystyle R_{\text{XX}}(\tau )}
4503:
3954:{\displaystyle \textstyle 4.\ since}
29:
6778:
6722:Trends in Adaptive Array Processing
6696:
6672:
6630:
6611:
4633:where the autocorrelation function
4461:Correlation spectrometers like the
145:enhance the signal to noise ratio (
103:that are spatially separated, e.g.
13:
7129:Multidimensional signal processing
7057:Krim, H.; Viberg, M. (July 1996).
6796:Krim, Hamid; Viberg, Mats (1995),
4600:
4548:
4543:
2652:
49:it lacks sufficient corresponding
14:
7140:
4845:to produce the cross-correlation
6820:Parsons, Aaron; Backer, Donald;
6761:"Improving IMS array processing"
6374:
6362:
6353:
6331:
6319:
6307:
6299:
6280:
6268:
6256:
6239:
6212:
6182:
6176:
6153:
6139:
6112:
5994:
5988:
5983:
5975:
5960:{\displaystyle \mathbf {u} _{1}}
5947:
5924:
5892:
5852:
5811:
5762:
5733:
5727:
5704:
5679:
5650:
5644:
5612:
5585:
5555:
5533:
5500:
5477:
5442:
5407:
5395:
5378:
5358:
5352:
5336:
5321:
5286:
5267:
5256:
5247:
5239:
5220:
5184:
5084:{\displaystyle \mathbf {R} _{v}}
5071:
5046:
5017:
5011:
4982:
4973:
4949:
4910:{\displaystyle S_{\text{XY}}(f)}
4494:{\displaystyle S_{\text{XX}}(f)}
2551:
2324:
2275:
2235:
2208:
2096:
2011:
1885:
1873:
1867:
1191:
1176:
947:
854:
761:
736:
728:
714:
706:
629:
34:
7066:IEEE Signal Processing Magazine
6975:
6930:
6891:
6813:
5148:{\displaystyle \sigma _{n}^{2}}
5116:{\displaystyle \sigma _{s}^{2}}
4841:
4115:{\displaystyle \textstyle Then}
206:
6904:IEEE Signal Processing Letters
6803:
6753:
6554:Space-time adaptive processing
6475:
6453:
6421:
6399:
6346:
6303:
6295:
6252:
6243:
6204:By right and left multiplying
6143:
6104:is the dominant eigenvalue of
5967:of the eigen-decomposition of
5869:
5862:
5831:
5824:
5815:
5767:
5708:
5684:
5625:
5616:
5325:
5272:
5251:
4904:
4898:
4868:
4862:
4826:
4820:
4769:
4757:
4744:
4738:
4717:
4711:
4656:
4650:
4593:
4578:
4569:
4563:
4529:
4523:
4488:
4482:
4420:
4417:
4404:
4380:
4367:
4354:
4346:
4333:
4196:
4183:
4153:
4139:
4071:
4058:
4028:
4014:
3992:
3979:
3907:
3894:
3839:
3826:
3663:
3657:
3644:
3631:
3618:
3566:
3537:
3477:
3471:
3438:
3409:
3226:
3197:
3137:
3131:
3098:
3069:
2910:
2863:
2643:
2637:
2612:
2606:
2571:
2565:
2295:
2289:
2254:
2248:
2182:
2176:
1409:
1396:
1323:
1310:
1281:
1268:
1207:
1201:
1186:
1180:
1019:
1016:
1003:
973:
960:
954:
926:
923:
910:
880:
867:
861:
833:
830:
817:
787:
774:
768:
724:
718:
681:
675:
666:
660:
654:
648:
639:
633:
602:
596:
547:{\displaystyle a(\theta _{k})}
541:
528:
503:
497:
465:
459:
430:
424:
415:
409:
396:
383:
353:
347:
1:
6584:
6506:by selecting the appropriate
4937:Projecting out the interferer
1025:{\displaystyle \mathbf {S} =}
932:{\displaystyle \mathbf {N} =}
839:{\displaystyle \mathbf {X} =}
6662:Spectral Analysis of Signals
6624:MIMO Radar Signal Processing
6219:{\displaystyle \mathbf {R} }
6119:{\displaystyle \mathbf {R} }
6097:{\displaystyle \lambda _{1}}
5931:{\displaystyle \mathbf {a} }
5592:{\displaystyle \mathbf {R} }
5562:{\displaystyle \mathbf {a} }
5540:{\displaystyle \mathbf {R} }
5484:{\displaystyle \mathbf {a} }
4956:{\displaystyle \mathbf {a} }
4793:
7:
7103:array processing courseware
6763:. Norsar.no. Archived from
6690:Robust Adaptive Beamforming
6542:
4623:
574:{\displaystyle \theta _{k}}
10:
7145:
7032:
6529:
4921:Example: spatial filtering
4452:Discrete Fourier Transform
2930:Parametric–based solutions
1074:b. Plane wave propagation.
18:
7048:Van Trees, H. L. (2002).
4437:Deterministic ML approach
250:Communications (wireless)
7050:Optimum Array Processing
6737:. NORSAR. Archived from
6692:. USA: J Wiley&Sons.
6626:. USA: J Wiley&Sons.
6606:Spatial Array Processing
5491:is generally not known,
5168:{\displaystyle \dagger }
5155:is the noise power, and
4832:{\displaystyle V_{Y}(t)}
4463:Michelson interferometer
4446:Correlation spectrometer
1615:Subspace-based technique
1097:Spectral–based solutions
509:{\displaystyle s_{k}(t)}
216:Radar and Sonar Systems:
19:Not to be confused with
7041:Array Signal Processing
6519:{\displaystyle \alpha }
4881:and the cross-spectrum
64:more precise citations.
6884:March 7, 2016, at the
6520:
6500:
6428:
6220:
6196:
6120:
6098:
6071:
6008:
5961:
5932:
5900:
5790:
5593:
5563:
5541:
5519:
5485:
5461:
5300:
5203:
5169:
5149:
5117:
5085:
5054:
4957:
4933:
4911:
4875:
4833:
4781:
4683:
4663:
4611:
4495:
4428:
4285:
4204:
4116:
4085:
3955:
3915:
3783:
3671:
3499:
3374:
3274:
3159:
3034:
2939:Stochastic ML approach
2917:
2916:{\displaystyle E_{n}=}
2833:
2737:
2660:
2411:
2117:
1975:
1934:
1839:
1591:
1490:
1331:
1215:
1174:
1026:
933:
840:
744:
689:
609:
575:
548:
510:
472:
438:
379:
309:
266:
242:
199:
6521:
6501:
6429:
6221:
6197:
6121:
6099:
6072:
6009:
5962:
5933:
5901:
5791:
5594:
5564:
5542:
5520:
5486:
5462:
5301:
5204:
5170:
5150:
5118:
5086:
5055:
4958:
4931:
4912:
4876:
4834:
4782:
4684:
4682:{\displaystyle \tau }
4664:
4612:
4496:
4429:
4286:
4205:
4117:
4086:
3956:
3916:
3784:
3672:
3500:
3375:
3275:
3160:
3035:
2918:
2834:
2738:
2661:
2412:
2118:
1976:
1914:
1840:
1592:
1491:
1332:
1216:
1154:
1105:Beamforming technique
1085:Estimation techniques
1027:
934:
841:
745:
690:
610:
576:
549:
511:
473:
439:
359:
307:
264:
240:
197:
185:direction of arrivals
6668:. NJ: Prentice Hall.
6510:
6440:
6232:
6208:
6132:
6108:
6081:
6018:
5971:
5942:
5920:
5804:
5605:
5581:
5551:
5529:
5495:
5473:
5314:
5215:
5179:
5159:
5127:
5095:
5066:
4969:
4945:
4885:
4849:
4807:
4698:
4673:
4637:
4510:
4469:
4295:
4214:
4126:
4095:
3965:
3925:
3793:
3681:
3509:
3384:
3284:
3169:
3044:
2955:
2847:
2747:
2670:
2421:
2127:
1985:
1849:
1638:
1500:
1341:
1225:
1121:
943:
850:
757:
702:
624:
615:is the noise vector.
608:{\displaystyle n(t)}
590:
558:
522:
484:
471:{\displaystyle x(t)}
453:
340:
278:Medical applications
156:track moving sources
25:Array data structure
7083:on 9 September 2013
7006:2000ApJS..131..355L
6916:2002ISPL....9...64R
6848:2008PASP..120.1207P
6495:
6388:
6345:
6294:
6174:
6066:
6035:
5760:
5725:
5677:
5642:
5514:
5456:
5439:
5421:
5392:
5372:
5350:
5234:
5198:
5144:
5112:
5044:
5009:
4552:
4400:
4329:
4179:
4054:
3890:
3588:
3248:
2827:
2799:
2765:
2561:
2285:
1969:
1478:
187:, and their signal
7052:. New York: Wiley.
6832:(873): 1207–1221.
6659:, R Moses (2005).
6516:
6496:
6481:
6424:
6372:
6329:
6278:
6216:
6192:
6160:
6116:
6094:
6067:
6052:
6021:
6004:
5957:
5928:
5896:
5786:
5746:
5711:
5663:
5628:
5589:
5559:
5537:
5515:
5498:
5481:
5457:
5440:
5425:
5405:
5376:
5356:
5334:
5296:
5218:
5199:
5182:
5165:
5145:
5130:
5113:
5098:
5081:
5050:
5030:
4995:
4953:
4934:
4907:
4871:
4829:
4777:
4679:
4659:
4607:
4535:
4491:
4424:
4423:
4383:
4312:
4281:
4280:
4200:
4199:
4162:
4112:
4111:
4081:
4080:
4037:
3951:
3950:
3911:
3910:
3873:
3779:
3778:
3667:
3666:
3574:
3495:
3494:
3370:
3369:
3270:
3269:
3234:
3155:
3154:
3030:
3029:
2913:
2842:eigenvector matrix
2829:
2828:
2813:
2785:
2751:
2733:
2732:
2656:
2655:
2545:
2407:
2406:
2269:
2113:
2112:
1971:
1970:
1955:
1835:
1834:
1587:
1586:
1486:
1485:
1466:
1327:
1326:
1211:
1210:
1035:Problem definition
1022:
929:
836:
740:
685:
684:
605:
571:
544:
506:
468:
434:
433:
313:Other applications
310:
267:
243:
200:
7074:10.1109/79.526899
6961:10.1109/18.857787
6924:10.1109/97.991140
6574:Bartlett's method
6246:
6146:
5884:
5846:
5818:
5782:
5699:
5619:
5573:Spatial whitening
5328:
4895:
4859:
4801:
4800:
4708:
4647:
4631:
4630:
4560:
4520:
4479:
4249:
4223:
3934:
3856:
3847:
3759:
3750:
3738:
3690:
3573:
3445:
3347:
3317:
3305:
3293:
3233:
3105:
3001:
2992:
2979:
2964:
2948:Approach overview
2718:
2709:
2697:
2679:
2647:
2602:
2593:
2523:
2508:
2502:
2475:
2463:
2451:
2430:
2384:
2351:
2345:
2336:
2321:
2303:
2268:
2259:
2232:
2223:
2187:
2172:
2154:
2136:
1994:
1791:
1758:
1725:
1716:
1674:
1647:
1631:Approach overview
1605:covariance matrix
1555:
1539:
1509:
1465:
1438:
1426:
1414:
1392:
1383:
1365:
1350:
1264:
1234:
1152:
1130:
1114:Approach overview
163:Estimation theory
97:signal processing
90:
89:
82:
7136:
7092:
7090:
7088:
7082:
7076:. Archived from
7063:
7053:
7044:
7043:. Prentice Hall.
7026:
7025:
6999:
6997:astro-ph/0005359
6979:
6973:
6972:
6954:
6952:astro-ph/0008239
6945:(5): 1730–1747.
6934:
6928:
6927:
6895:
6889:
6874:
6868:
6867:
6841:
6817:
6811:
6807:
6801:
6800:
6793:
6776:
6775:
6773:
6772:
6757:
6751:
6750:
6748:
6746:
6731:
6725:
6724:
6717:
6694:
6693:
6681:
6670:
6669:
6667:
6653:
6628:
6627:
6615:
6609:
6602:
6525:
6523:
6522:
6517:
6505:
6503:
6502:
6497:
6494:
6489:
6474:
6473:
6452:
6451:
6433:
6431:
6430:
6425:
6420:
6419:
6398:
6397:
6387:
6382:
6377:
6371:
6370:
6365:
6356:
6344:
6339:
6334:
6328:
6327:
6322:
6310:
6302:
6293:
6288:
6283:
6277:
6276:
6271:
6259:
6248:
6247:
6242:
6237:
6225:
6223:
6222:
6217:
6215:
6201:
6199:
6198:
6193:
6191:
6190:
6185:
6179:
6173:
6168:
6156:
6148:
6147:
6142:
6137:
6125:
6123:
6122:
6117:
6115:
6103:
6101:
6100:
6095:
6093:
6092:
6076:
6074:
6073:
6068:
6065:
6060:
6048:
6047:
6034:
6029:
6013:
6011:
6010:
6005:
6003:
6002:
5997:
5991:
5986:
5978:
5966:
5964:
5963:
5958:
5956:
5955:
5950:
5937:
5935:
5934:
5929:
5927:
5905:
5903:
5902:
5897:
5895:
5887:
5886:
5885:
5877:
5861:
5860:
5855:
5849:
5848:
5847:
5839:
5820:
5819:
5814:
5809:
5795:
5793:
5792:
5787:
5785:
5784:
5783:
5775:
5765:
5759:
5754:
5742:
5741:
5736:
5730:
5724:
5719:
5707:
5702:
5701:
5700:
5692:
5682:
5676:
5671:
5659:
5658:
5653:
5647:
5641:
5636:
5621:
5620:
5615:
5610:
5598:
5596:
5595:
5590:
5588:
5568:
5566:
5565:
5560:
5558:
5546:
5544:
5543:
5538:
5536:
5524:
5522:
5521:
5516:
5513:
5508:
5503:
5490:
5488:
5487:
5482:
5480:
5466:
5464:
5463:
5458:
5455:
5450:
5445:
5438:
5433:
5420:
5415:
5410:
5404:
5403:
5398:
5391:
5386:
5381:
5371:
5366:
5361:
5355:
5349:
5344:
5339:
5330:
5329:
5324:
5319:
5305:
5303:
5302:
5297:
5295:
5294:
5289:
5283:
5282:
5270:
5265:
5264:
5259:
5250:
5242:
5233:
5228:
5223:
5208:
5206:
5205:
5200:
5197:
5192:
5187:
5174:
5172:
5171:
5166:
5154:
5152:
5151:
5146:
5143:
5138:
5122:
5120:
5119:
5114:
5111:
5106:
5090:
5088:
5087:
5082:
5080:
5079:
5074:
5059:
5057:
5056:
5051:
5049:
5043:
5038:
5026:
5025:
5020:
5014:
5008:
5003:
4991:
4990:
4985:
4976:
4962:
4960:
4959:
4954:
4952:
4916:
4914:
4913:
4908:
4897:
4896:
4893:
4880:
4878:
4877:
4872:
4861:
4860:
4857:
4838:
4836:
4835:
4830:
4819:
4818:
4795:
4786:
4784:
4783:
4778:
4776:
4772:
4756:
4755:
4737:
4736:
4710:
4709:
4706:
4692:
4688:
4686:
4685:
4680:
4668:
4666:
4665:
4660:
4649:
4648:
4645:
4625:
4616:
4614:
4613:
4608:
4603:
4562:
4561:
4558:
4551:
4546:
4522:
4521:
4518:
4504:
4500:
4498:
4497:
4492:
4481:
4480:
4477:
4433:
4431:
4430:
4425:
4416:
4415:
4399:
4391:
4379:
4378:
4366:
4365:
4353:
4345:
4344:
4328:
4320:
4308:
4307:
4290:
4288:
4287:
4282:
4247:
4243:
4221:
4209:
4207:
4206:
4201:
4195:
4194:
4178:
4170:
4161:
4160:
4151:
4150:
4121:
4119:
4118:
4113:
4090:
4088:
4087:
4082:
4070:
4069:
4053:
4045:
4036:
4035:
4026:
4025:
4004:
4003:
3991:
3990:
3978:
3977:
3960:
3958:
3957:
3952:
3932:
3920:
3918:
3917:
3912:
3906:
3905:
3889:
3881:
3866:
3865:
3854:
3845:
3838:
3837:
3816:
3815:
3806:
3805:
3788:
3786:
3785:
3780:
3757:
3748:
3736:
3688:
3676:
3674:
3673:
3668:
3656:
3655:
3643:
3642:
3630:
3629:
3608:
3607:
3598:
3597:
3587:
3582:
3571:
3570:
3569:
3559:
3558:
3549:
3548:
3536:
3535:
3504:
3502:
3501:
3496:
3490:
3489:
3484:
3480:
3467:
3466:
3443:
3442:
3441:
3431:
3430:
3421:
3420:
3408:
3407:
3379:
3377:
3376:
3371:
3345:
3315:
3303:
3291:
3279:
3277:
3276:
3271:
3268:
3267:
3258:
3257:
3247:
3242:
3231:
3230:
3229:
3219:
3218:
3209:
3208:
3196:
3195:
3164:
3162:
3161:
3156:
3150:
3149:
3144:
3140:
3127:
3126:
3103:
3102:
3101:
3091:
3090:
3081:
3080:
3068:
3067:
3039:
3037:
3036:
3031:
2999:
2990:
2989:
2988:
2977:
2962:
2922:
2920:
2919:
2914:
2909:
2908:
2875:
2874:
2859:
2858:
2840:where the noise
2838:
2836:
2835:
2830:
2826:
2821:
2812:
2811:
2798:
2793:
2784:
2783:
2764:
2759:
2742:
2740:
2739:
2734:
2728:
2727:
2716:
2707:
2695:
2677:
2665:
2663:
2662:
2657:
2648:
2646:
2633:
2632:
2619:
2600:
2591:
2584:
2583:
2578:
2574:
2560:
2555:
2554:
2521:
2506:
2500:
2473:
2461:
2449:
2428:
2416:
2414:
2413:
2408:
2382:
2349:
2343:
2334:
2333:
2332:
2327:
2319:
2301:
2284:
2279:
2278:
2266:
2257:
2244:
2243:
2238:
2230:
2221:
2217:
2216:
2211:
2185:
2170:
2152:
2134:
2122:
2120:
2119:
2114:
2105:
2104:
2099:
2072:
2071:
2014:
1992:
1980:
1978:
1977:
1972:
1968:
1963:
1954:
1953:
1944:
1943:
1933:
1928:
1907:
1906:
1894:
1893:
1888:
1882:
1881:
1876:
1870:
1862:
1861:
1844:
1842:
1841:
1836:
1789:
1756:
1723:
1714:
1672:
1645:
1596:
1594:
1593:
1588:
1553:
1549:
1548:
1537:
1507:
1495:
1493:
1492:
1487:
1474:
1463:
1436:
1424:
1412:
1408:
1407:
1390:
1381:
1363:
1348:
1336:
1334:
1333:
1328:
1322:
1321:
1306:
1305:
1296:
1295:
1280:
1279:
1262:
1232:
1220:
1218:
1217:
1212:
1200:
1199:
1194:
1179:
1173:
1168:
1153:
1145:
1140:
1139:
1128:
1051:
1031:
1029:
1028:
1023:
1015:
1014:
972:
971:
950:
938:
936:
935:
930:
922:
921:
879:
878:
857:
845:
843:
842:
837:
829:
828:
786:
785:
764:
749:
747:
746:
741:
739:
731:
717:
709:
694:
692:
691:
686:
632:
614:
612:
611:
606:
580:
578:
577:
572:
570:
569:
553:
551:
550:
545:
540:
539:
515:
513:
512:
507:
496:
495:
477:
475:
474:
469:
443:
441:
440:
435:
408:
407:
395:
394:
378:
373:
129:machine learning
125:wave propagation
93:Array processing
85:
78:
74:
71:
65:
60:this article by
51:inline citations
38:
37:
30:
7144:
7143:
7139:
7138:
7137:
7135:
7134:
7133:
7114:
7113:
7101:A.B. Gershman,
7086:
7084:
7080:
7061:
7035:
7030:
7029:
6980:
6976:
6935:
6931:
6896:
6892:
6886:Wayback Machine
6875:
6871:
6822:Siemion, Andrew
6818:
6814:
6808:
6804:
6794:
6779:
6770:
6768:
6759:
6758:
6754:
6744:
6742:
6741:on 20 June 2013
6733:
6732:
6728:
6718:
6697:
6682:
6673:
6665:
6654:
6631:
6616:
6612:
6603:
6592:
6587:
6545:
6532:
6511:
6508:
6507:
6490:
6485:
6469:
6465:
6447:
6443:
6441:
6438:
6437:
6415:
6411:
6393:
6389:
6383:
6378:
6373:
6366:
6361:
6360:
6352:
6340:
6335:
6330:
6323:
6318:
6317:
6306:
6298:
6289:
6284:
6279:
6272:
6267:
6266:
6255:
6238:
6236:
6235:
6233:
6230:
6229:
6211:
6209:
6206:
6205:
6186:
6181:
6180:
6175:
6169:
6164:
6152:
6138:
6136:
6135:
6133:
6130:
6129:
6111:
6109:
6106:
6105:
6088:
6084:
6082:
6079:
6078:
6061:
6056:
6043:
6039:
6030:
6025:
6019:
6016:
6015:
5998:
5993:
5992:
5987:
5982:
5974:
5972:
5969:
5968:
5951:
5946:
5945:
5943:
5940:
5939:
5923:
5921:
5918:
5917:
5914:
5891:
5876:
5872:
5868:
5856:
5851:
5850:
5838:
5834:
5830:
5810:
5808:
5807:
5805:
5802:
5801:
5774:
5770:
5766:
5761:
5755:
5750:
5737:
5732:
5731:
5726:
5720:
5715:
5703:
5691:
5687:
5683:
5678:
5672:
5667:
5654:
5649:
5648:
5643:
5637:
5632:
5611:
5609:
5608:
5606:
5603:
5602:
5584:
5582:
5579:
5578:
5575:
5554:
5552:
5549:
5548:
5532:
5530:
5527:
5526:
5509:
5504:
5499:
5496:
5493:
5492:
5476:
5474:
5471:
5470:
5451:
5446:
5441:
5434:
5429:
5416:
5411:
5406:
5399:
5394:
5393:
5387:
5382:
5377:
5367:
5362:
5357:
5351:
5345:
5340:
5335:
5320:
5318:
5317:
5315:
5312:
5311:
5290:
5285:
5284:
5275:
5271:
5266:
5260:
5255:
5254:
5246:
5238:
5229:
5224:
5219:
5216:
5213:
5212:
5193:
5188:
5183:
5180:
5177:
5176:
5160:
5157:
5156:
5139:
5134:
5128:
5125:
5124:
5107:
5102:
5096:
5093:
5092:
5075:
5070:
5069:
5067:
5064:
5063:
5045:
5039:
5034:
5021:
5016:
5015:
5010:
5004:
4999:
4986:
4981:
4980:
4972:
4970:
4967:
4966:
4948:
4946:
4943:
4942:
4939:
4923:
4892:
4888:
4886:
4883:
4882:
4856:
4852:
4850:
4847:
4846:
4814:
4810:
4808:
4805:
4804:
4751:
4747:
4732:
4728:
4727:
4723:
4705:
4701:
4699:
4696:
4695:
4674:
4671:
4670:
4644:
4640:
4638:
4635:
4634:
4599:
4557:
4553:
4547:
4539:
4517:
4513:
4511:
4508:
4507:
4476:
4472:
4470:
4467:
4466:
4448:
4439:
4411:
4407:
4392:
4387:
4374:
4370:
4361:
4357:
4349:
4340:
4336:
4321:
4316:
4303:
4299:
4296:
4293:
4292:
4291:
4236:
4215:
4212:
4211:
4210:
4190:
4186:
4171:
4166:
4156:
4152:
4146:
4142:
4127:
4124:
4123:
4122:
4096:
4093:
4092:
4091:
4065:
4061:
4046:
4041:
4031:
4027:
4021:
4017:
3999:
3995:
3986:
3982:
3973:
3969:
3966:
3963:
3962:
3961:
3926:
3923:
3922:
3921:
3901:
3897:
3882:
3877:
3861:
3857:
3833:
3829:
3811:
3807:
3801:
3797:
3794:
3791:
3790:
3789:
3682:
3679:
3678:
3677:
3651:
3647:
3638:
3634:
3625:
3621:
3603:
3599:
3593:
3589:
3583:
3578:
3554:
3550:
3544:
3540:
3531:
3527:
3526:
3522:
3510:
3507:
3506:
3505:
3485:
3462:
3458:
3457:
3453:
3452:
3426:
3422:
3416:
3412:
3403:
3399:
3398:
3394:
3385:
3382:
3381:
3380:
3285:
3282:
3281:
3280:
3263:
3259:
3253:
3249:
3243:
3238:
3214:
3210:
3204:
3200:
3191:
3187:
3186:
3182:
3170:
3167:
3166:
3165:
3145:
3122:
3118:
3117:
3113:
3112:
3086:
3082:
3076:
3072:
3063:
3059:
3058:
3054:
3045:
3042:
3041:
3040:
2984:
2980:
2956:
2953:
2952:
2951:
2945:
2941:
2932:
2904:
2900:
2870:
2866:
2854:
2850:
2848:
2845:
2844:
2839:
2822:
2817:
2807:
2803:
2794:
2789:
2779:
2775:
2760:
2755:
2748:
2745:
2744:
2743:
2723:
2719:
2671:
2668:
2667:
2666:
2628:
2624:
2623:
2618:
2579:
2556:
2550:
2549:
2544:
2540:
2539:
2422:
2419:
2418:
2417:
2328:
2323:
2322:
2280:
2274:
2273:
2239:
2234:
2233:
2212:
2207:
2206:
2128:
2125:
2124:
2123:
2100:
2095:
2094:
2067:
2063:
2010:
1986:
1983:
1982:
1981:
1964:
1959:
1949:
1945:
1939:
1935:
1929:
1918:
1902:
1898:
1889:
1884:
1883:
1877:
1872:
1871:
1866:
1857:
1853:
1850:
1847:
1846:
1845:
1639:
1636:
1635:
1634:
1621:
1617:
1598:
1597:
1544:
1540:
1501:
1498:
1497:
1496:
1470:
1403:
1399:
1342:
1339:
1338:
1337:
1317:
1313:
1301:
1297:
1291:
1287:
1275:
1271:
1226:
1223:
1222:
1221:
1195:
1190:
1189:
1175:
1169:
1158:
1144:
1135:
1131:
1122:
1119:
1118:
1117:
1111:
1107:
1099:
1087:
1049:
1037:
1010:
1006:
967:
963:
946:
944:
941:
940:
939:
917:
913:
874:
870:
853:
851:
848:
847:
846:
824:
820:
781:
777:
760:
758:
755:
754:
753:
735:
727:
713:
705:
703:
700:
699:
698:
628:
625:
622:
621:
620:
591:
588:
587:
565:
561:
559:
556:
555:
535:
531:
523:
520:
519:
491:
487:
485:
482:
481:
454:
451:
450:
403:
399:
390:
386:
374:
363:
341:
338:
337:
336:
324:
209:
131:applications a
86:
75:
69:
66:
56:Please help to
55:
39:
35:
28:
21:Array processor
17:
12:
11:
5:
7142:
7132:
7131:
7126:
7112:
7111:
7108:
7105:
7099:
7096:
7093:
7054:
7045:
7034:
7031:
7028:
7027:
7014:10.1086/317360
6990:(1): 355–373.
6974:
6929:
6890:
6869:
6856:10.1086/593053
6812:
6802:
6777:
6752:
6726:
6695:
6688:(Eds) (2006).
6671:
6629:
6622:(Eds) (2009).
6610:
6589:
6588:
6586:
6583:
6582:
6581:
6576:
6571:
6569:Welch's method
6566:
6564:Matched filter
6561:
6556:
6551:
6544:
6541:
6531:
6528:
6515:
6493:
6488:
6484:
6480:
6477:
6472:
6468:
6464:
6461:
6458:
6455:
6450:
6446:
6423:
6418:
6414:
6410:
6407:
6404:
6401:
6396:
6392:
6386:
6381:
6376:
6369:
6364:
6359:
6355:
6351:
6348:
6343:
6338:
6333:
6326:
6321:
6316:
6313:
6309:
6305:
6301:
6297:
6292:
6287:
6282:
6275:
6270:
6265:
6262:
6258:
6254:
6251:
6245:
6241:
6214:
6189:
6184:
6178:
6172:
6167:
6163:
6159:
6155:
6151:
6145:
6141:
6114:
6091:
6087:
6064:
6059:
6055:
6051:
6046:
6042:
6038:
6033:
6028:
6024:
6001:
5996:
5990:
5985:
5981:
5977:
5954:
5949:
5926:
5913:
5910:
5894:
5890:
5883:
5880:
5875:
5871:
5867:
5864:
5859:
5854:
5845:
5842:
5837:
5833:
5829:
5826:
5823:
5817:
5813:
5781:
5778:
5773:
5769:
5764:
5758:
5753:
5749:
5745:
5740:
5735:
5729:
5723:
5718:
5714:
5710:
5706:
5698:
5695:
5690:
5686:
5681:
5675:
5670:
5666:
5662:
5657:
5652:
5646:
5640:
5635:
5631:
5627:
5624:
5618:
5614:
5587:
5574:
5571:
5557:
5535:
5512:
5507:
5502:
5479:
5454:
5449:
5444:
5437:
5432:
5428:
5424:
5419:
5414:
5409:
5402:
5397:
5390:
5385:
5380:
5375:
5370:
5365:
5360:
5354:
5348:
5343:
5338:
5333:
5327:
5323:
5293:
5288:
5281:
5278:
5274:
5269:
5263:
5258:
5253:
5249:
5245:
5241:
5237:
5232:
5227:
5222:
5196:
5191:
5186:
5164:
5142:
5137:
5133:
5110:
5105:
5101:
5078:
5073:
5048:
5042:
5037:
5033:
5029:
5024:
5019:
5013:
5007:
5002:
4998:
4994:
4989:
4984:
4979:
4975:
4951:
4938:
4935:
4922:
4919:
4906:
4903:
4900:
4891:
4870:
4867:
4864:
4855:
4828:
4825:
4822:
4817:
4813:
4799:
4798:
4789:
4787:
4775:
4771:
4768:
4765:
4762:
4759:
4754:
4750:
4746:
4743:
4740:
4735:
4731:
4726:
4722:
4719:
4716:
4713:
4704:
4678:
4658:
4655:
4652:
4643:
4629:
4628:
4619:
4617:
4606:
4602:
4598:
4595:
4592:
4589:
4586:
4583:
4580:
4577:
4574:
4571:
4568:
4565:
4556:
4550:
4545:
4542:
4538:
4534:
4531:
4528:
4525:
4516:
4490:
4487:
4484:
4475:
4447:
4444:
4438:
4435:
4422:
4419:
4414:
4410:
4406:
4403:
4398:
4395:
4390:
4386:
4382:
4377:
4373:
4369:
4364:
4360:
4356:
4352:
4348:
4343:
4339:
4335:
4332:
4327:
4324:
4319:
4315:
4311:
4306:
4302:
4279:
4276:
4273:
4270:
4267:
4264:
4261:
4258:
4255:
4252:
4246:
4242:
4239:
4235:
4232:
4229:
4226:
4220:
4198:
4193:
4189:
4185:
4182:
4177:
4174:
4169:
4165:
4159:
4155:
4149:
4145:
4141:
4138:
4135:
4132:
4110:
4107:
4104:
4101:
4079:
4076:
4073:
4068:
4064:
4060:
4057:
4052:
4049:
4044:
4040:
4034:
4030:
4024:
4020:
4016:
4013:
4010:
4007:
4002:
3998:
3994:
3989:
3985:
3981:
3976:
3972:
3949:
3946:
3943:
3940:
3937:
3931:
3909:
3904:
3900:
3896:
3893:
3888:
3885:
3880:
3876:
3872:
3869:
3864:
3860:
3853:
3850:
3844:
3841:
3836:
3832:
3828:
3825:
3822:
3819:
3814:
3810:
3804:
3800:
3777:
3774:
3771:
3768:
3765:
3762:
3756:
3753:
3747:
3744:
3741:
3735:
3732:
3729:
3726:
3723:
3720:
3717:
3714:
3711:
3708:
3705:
3702:
3699:
3696:
3693:
3687:
3665:
3662:
3659:
3654:
3650:
3646:
3641:
3637:
3633:
3628:
3624:
3620:
3617:
3614:
3611:
3606:
3602:
3596:
3592:
3586:
3581:
3577:
3568:
3565:
3562:
3557:
3553:
3547:
3543:
3539:
3534:
3530:
3525:
3521:
3518:
3515:
3493:
3488:
3483:
3479:
3476:
3473:
3470:
3465:
3461:
3456:
3451:
3448:
3440:
3437:
3434:
3429:
3425:
3419:
3415:
3411:
3406:
3402:
3397:
3393:
3390:
3368:
3365:
3362:
3359:
3356:
3353:
3350:
3344:
3341:
3338:
3335:
3332:
3329:
3326:
3323:
3320:
3314:
3311:
3308:
3302:
3299:
3296:
3290:
3266:
3262:
3256:
3252:
3246:
3241:
3237:
3228:
3225:
3222:
3217:
3213:
3207:
3203:
3199:
3194:
3190:
3185:
3181:
3178:
3175:
3153:
3148:
3143:
3139:
3136:
3133:
3130:
3125:
3121:
3116:
3111:
3108:
3100:
3097:
3094:
3089:
3085:
3079:
3075:
3071:
3066:
3062:
3057:
3053:
3050:
3028:
3025:
3022:
3019:
3016:
3013:
3010:
3007:
3004:
2998:
2995:
2987:
2983:
2976:
2973:
2970:
2967:
2961:
2940:
2937:
2931:
2928:
2912:
2907:
2903:
2899:
2896:
2893:
2890:
2887:
2884:
2881:
2878:
2873:
2869:
2865:
2862:
2857:
2853:
2825:
2820:
2816:
2810:
2806:
2802:
2797:
2792:
2788:
2782:
2778:
2774:
2771:
2768:
2763:
2758:
2754:
2731:
2726:
2722:
2715:
2712:
2706:
2703:
2700:
2694:
2691:
2688:
2685:
2682:
2676:
2654:
2651:
2645:
2642:
2639:
2636:
2631:
2627:
2622:
2617:
2614:
2611:
2608:
2605:
2599:
2596:
2590:
2587:
2582:
2577:
2573:
2570:
2567:
2564:
2559:
2553:
2548:
2543:
2538:
2535:
2532:
2529:
2526:
2520:
2517:
2514:
2511:
2505:
2499:
2496:
2493:
2490:
2487:
2484:
2481:
2478:
2472:
2469:
2466:
2460:
2457:
2454:
2448:
2445:
2442:
2439:
2436:
2433:
2427:
2405:
2402:
2399:
2396:
2393:
2390:
2387:
2381:
2378:
2375:
2372:
2369:
2366:
2363:
2360:
2357:
2354:
2348:
2342:
2339:
2331:
2326:
2318:
2315:
2312:
2309:
2306:
2300:
2297:
2294:
2291:
2288:
2283:
2277:
2272:
2265:
2262:
2256:
2253:
2250:
2247:
2242:
2237:
2229:
2226:
2220:
2215:
2210:
2205:
2202:
2199:
2196:
2193:
2190:
2184:
2181:
2178:
2175:
2169:
2166:
2163:
2160:
2157:
2151:
2148:
2145:
2142:
2139:
2133:
2111:
2108:
2103:
2098:
2093:
2090:
2087:
2084:
2081:
2078:
2075:
2070:
2066:
2062:
2059:
2056:
2053:
2050:
2047:
2044:
2041:
2038:
2035:
2032:
2029:
2026:
2023:
2020:
2017:
2013:
2009:
2006:
2003:
2000:
1997:
1991:
1967:
1962:
1958:
1952:
1948:
1942:
1938:
1932:
1927:
1924:
1921:
1917:
1913:
1910:
1905:
1901:
1897:
1892:
1887:
1880:
1875:
1869:
1865:
1860:
1856:
1833:
1830:
1827:
1824:
1821:
1818:
1815:
1812:
1809:
1806:
1803:
1800:
1797:
1794:
1788:
1785:
1782:
1779:
1776:
1773:
1770:
1767:
1764:
1761:
1755:
1752:
1749:
1746:
1743:
1740:
1737:
1734:
1731:
1728:
1722:
1719:
1713:
1710:
1707:
1704:
1701:
1698:
1695:
1692:
1689:
1686:
1683:
1680:
1677:
1671:
1668:
1665:
1662:
1659:
1656:
1653:
1650:
1644:
1616:
1613:
1603:is the sample
1585:
1582:
1579:
1576:
1573:
1570:
1567:
1564:
1561:
1558:
1552:
1547:
1543:
1536:
1533:
1530:
1527:
1524:
1521:
1518:
1515:
1512:
1506:
1484:
1481:
1477:
1473:
1469:
1462:
1459:
1456:
1453:
1450:
1447:
1444:
1441:
1435:
1432:
1429:
1423:
1420:
1417:
1411:
1406:
1402:
1398:
1395:
1389:
1386:
1380:
1377:
1374:
1371:
1368:
1362:
1359:
1356:
1353:
1347:
1325:
1320:
1316:
1312:
1309:
1304:
1300:
1294:
1290:
1286:
1283:
1278:
1274:
1270:
1267:
1261:
1258:
1255:
1252:
1249:
1246:
1243:
1240:
1237:
1231:
1209:
1206:
1203:
1198:
1193:
1188:
1185:
1182:
1178:
1172:
1167:
1164:
1161:
1157:
1151:
1148:
1143:
1138:
1134:
1127:
1106:
1103:
1098:
1095:
1086:
1083:
1078:
1077:
1076:
1075:
1072:
1066:
1065:
1062:
1059:
1056:
1053:
1021:
1018:
1013:
1009:
1005:
1002:
999:
996:
993:
990:
987:
984:
981:
978:
975:
970:
966:
962:
959:
956:
953:
949:
928:
925:
920:
916:
912:
909:
906:
903:
900:
897:
894:
891:
888:
885:
882:
877:
873:
869:
866:
863:
860:
856:
835:
832:
827:
823:
819:
816:
813:
810:
807:
804:
801:
798:
795:
792:
789:
784:
780:
776:
773:
770:
767:
763:
738:
734:
730:
726:
723:
720:
716:
712:
708:
683:
680:
677:
674:
671:
668:
665:
662:
659:
656:
653:
650:
647:
644:
641:
638:
635:
631:
617:
616:
604:
601:
598:
595:
585:
582:
568:
564:
543:
538:
534:
530:
527:
517:
505:
502:
499:
494:
490:
479:
467:
464:
461:
458:
432:
429:
426:
423:
420:
417:
414:
411:
406:
402:
398:
393:
389:
385:
382:
377:
372:
369:
366:
362:
358:
355:
352:
349:
346:
323:
320:
315:
314:
298:
297:
289:
288:
280:
279:
252:
251:
218:
217:
208:
205:
158:
157:
154:
143:
117:accelerometers
109:seismic arrays
88:
87:
42:
40:
33:
15:
9:
6:
4:
3:
2:
7141:
7130:
7127:
7125:
7122:
7121:
7119:
7109:
7106:
7104:
7100:
7097:
7094:
7079:
7075:
7071:
7067:
7060:
7055:
7051:
7046:
7042:
7037:
7036:
7023:
7019:
7015:
7011:
7007:
7003:
6998:
6993:
6989:
6985:
6978:
6970:
6966:
6962:
6958:
6953:
6948:
6944:
6940:
6933:
6925:
6921:
6917:
6913:
6910:(12): 64–67.
6909:
6905:
6901:
6894:
6888:Andrew Harris
6887:
6883:
6880:
6879:
6873:
6865:
6861:
6857:
6853:
6849:
6845:
6840:
6835:
6831:
6827:
6823:
6816:
6806:
6799:
6792:
6790:
6788:
6786:
6784:
6782:
6767:on 2012-08-21
6766:
6762:
6756:
6740:
6736:
6730:
6723:
6716:
6714:
6712:
6710:
6708:
6706:
6704:
6702:
6700:
6691:
6687:
6680:
6678:
6676:
6664:
6663:
6658:
6652:
6650:
6648:
6646:
6644:
6642:
6640:
6638:
6636:
6634:
6625:
6621:
6614:
6607:
6601:
6599:
6597:
6595:
6590:
6580:
6577:
6575:
6572:
6570:
6567:
6565:
6562:
6560:
6557:
6555:
6552:
6550:
6547:
6546:
6540:
6536:
6527:
6513:
6491:
6486:
6482:
6478:
6470:
6466:
6462:
6459:
6456:
6448:
6444:
6434:
6416:
6412:
6408:
6405:
6402:
6394:
6390:
6384:
6379:
6367:
6357:
6349:
6341:
6336:
6324:
6314:
6311:
6290:
6285:
6273:
6263:
6260:
6249:
6227:
6202:
6187:
6170:
6165:
6161:
6157:
6149:
6127:
6089:
6085:
6062:
6057:
6053:
6049:
6044:
6040:
6036:
6031:
6026:
6022:
5999:
5979:
5952:
5909:
5906:
5888:
5881:
5878:
5873:
5865:
5857:
5843:
5840:
5835:
5827:
5821:
5799:
5796:
5779:
5776:
5771:
5756:
5751:
5747:
5743:
5738:
5721:
5716:
5712:
5696:
5693:
5688:
5673:
5668:
5664:
5660:
5655:
5638:
5633:
5629:
5622:
5600:
5570:
5510:
5505:
5467:
5452:
5447:
5435:
5430:
5426:
5422:
5417:
5412:
5400:
5388:
5383:
5373:
5368:
5363:
5346:
5341:
5331:
5309:
5306:
5291:
5279:
5276:
5261:
5243:
5235:
5230:
5225:
5210:
5194:
5189:
5162:
5140:
5135:
5131:
5108:
5103:
5099:
5076:
5060:
5040:
5035:
5031:
5027:
5022:
5005:
5000:
4996:
4992:
4987:
4977:
4964:
4930:
4926:
4918:
4901:
4889:
4865:
4853:
4844:
4843:
4823:
4815:
4811:
4797:
4790:
4788:
4773:
4766:
4763:
4760:
4752:
4748:
4741:
4733:
4729:
4724:
4720:
4714:
4702:
4694:
4693:
4690:
4676:
4653:
4641:
4627:
4620:
4618:
4604:
4596:
4590:
4587:
4584:
4581:
4575:
4572:
4566:
4554:
4540:
4536:
4532:
4526:
4514:
4506:
4505:
4502:
4485:
4473:
4464:
4459:
4457:
4453:
4443:
4434:
4412:
4408:
4401:
4396:
4393:
4388:
4384:
4375:
4371:
4362:
4358:
4350:
4341:
4337:
4330:
4325:
4322:
4317:
4313:
4309:
4304:
4300:
4277:
4274:
4271:
4268:
4265:
4262:
4259:
4256:
4253:
4250:
4244:
4240:
4237:
4233:
4230:
4227:
4224:
4218:
4191:
4187:
4180:
4175:
4172:
4167:
4163:
4157:
4147:
4143:
4136:
4133:
4130:
4108:
4105:
4102:
4099:
4077:
4074:
4066:
4062:
4055:
4050:
4047:
4042:
4038:
4032:
4022:
4018:
4011:
4008:
4005:
4000:
3996:
3987:
3983:
3974:
3970:
3947:
3944:
3941:
3938:
3935:
3929:
3902:
3898:
3891:
3886:
3883:
3878:
3874:
3870:
3867:
3862:
3858:
3851:
3848:
3842:
3834:
3830:
3823:
3820:
3817:
3812:
3808:
3802:
3798:
3775:
3772:
3769:
3766:
3763:
3760:
3754:
3751:
3745:
3742:
3739:
3733:
3730:
3727:
3724:
3721:
3718:
3715:
3712:
3709:
3706:
3703:
3700:
3697:
3694:
3691:
3685:
3660:
3652:
3648:
3639:
3635:
3626:
3622:
3615:
3612:
3609:
3604:
3600:
3594:
3590:
3584:
3579:
3575:
3563:
3560:
3555:
3551:
3545:
3541:
3532:
3528:
3523:
3519:
3516:
3513:
3486:
3481:
3474:
3468:
3463:
3459:
3454:
3446:
3435:
3432:
3427:
3423:
3417:
3413:
3404:
3400:
3395:
3391:
3388:
3366:
3363:
3360:
3357:
3354:
3351:
3348:
3342:
3339:
3336:
3333:
3330:
3327:
3324:
3321:
3318:
3312:
3309:
3306:
3300:
3297:
3294:
3288:
3264:
3260:
3254:
3250:
3244:
3239:
3235:
3223:
3220:
3215:
3211:
3205:
3201:
3192:
3188:
3183:
3179:
3176:
3173:
3146:
3141:
3134:
3128:
3123:
3119:
3114:
3106:
3095:
3092:
3087:
3083:
3077:
3073:
3064:
3060:
3055:
3051:
3048:
3026:
3023:
3020:
3017:
3014:
3011:
3008:
3005:
3002:
2996:
2993:
2985:
2981:
2974:
2971:
2968:
2965:
2959:
2950:
2949:
2936:
2927:
2923:
2905:
2901:
2897:
2894:
2891:
2888:
2885:
2882:
2879:
2876:
2871:
2867:
2860:
2855:
2851:
2843:
2823:
2818:
2814:
2808:
2804:
2800:
2795:
2790:
2786:
2780:
2776:
2772:
2769:
2766:
2761:
2756:
2752:
2729:
2724:
2720:
2713:
2710:
2704:
2701:
2698:
2692:
2689:
2686:
2683:
2680:
2674:
2649:
2640:
2634:
2629:
2625:
2620:
2615:
2609:
2603:
2597:
2594:
2588:
2585:
2580:
2575:
2568:
2562:
2557:
2546:
2541:
2536:
2533:
2530:
2527:
2524:
2518:
2515:
2512:
2509:
2503:
2497:
2494:
2491:
2488:
2485:
2482:
2479:
2476:
2470:
2467:
2464:
2458:
2455:
2452:
2446:
2443:
2440:
2437:
2434:
2431:
2425:
2403:
2400:
2397:
2394:
2391:
2388:
2385:
2379:
2376:
2373:
2370:
2367:
2364:
2361:
2358:
2355:
2352:
2346:
2340:
2337:
2329:
2316:
2313:
2310:
2307:
2304:
2298:
2292:
2286:
2281:
2270:
2263:
2260:
2251:
2245:
2240:
2227:
2224:
2213:
2200:
2197:
2194:
2191:
2188:
2179:
2173:
2167:
2164:
2161:
2158:
2155:
2149:
2146:
2143:
2140:
2137:
2131:
2109:
2101:
2088:
2085:
2082:
2079:
2076:
2068:
2064:
2060:
2057:
2054:
2051:
2048:
2045:
2042:
2039:
2033:
2030:
2027:
2024:
2021:
2018:
2004:
2001:
1998:
1995:
1989:
1965:
1960:
1956:
1950:
1946:
1940:
1936:
1930:
1925:
1922:
1919:
1915:
1911:
1908:
1903:
1899:
1895:
1890:
1878:
1863:
1858:
1854:
1831:
1828:
1825:
1822:
1819:
1816:
1813:
1810:
1807:
1804:
1801:
1798:
1795:
1792:
1786:
1783:
1780:
1777:
1774:
1771:
1768:
1765:
1762:
1759:
1753:
1750:
1747:
1744:
1741:
1738:
1735:
1732:
1729:
1726:
1720:
1717:
1711:
1708:
1705:
1702:
1699:
1696:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1669:
1666:
1663:
1660:
1657:
1654:
1651:
1648:
1642:
1633:
1632:
1627:
1625:
1612:
1610:
1606:
1602:
1583:
1580:
1577:
1574:
1571:
1568:
1565:
1562:
1559:
1556:
1550:
1545:
1541:
1534:
1531:
1528:
1525:
1522:
1519:
1516:
1513:
1510:
1504:
1482:
1479:
1475:
1471:
1467:
1460:
1457:
1454:
1451:
1448:
1445:
1442:
1439:
1433:
1430:
1427:
1421:
1418:
1415:
1404:
1400:
1393:
1387:
1384:
1378:
1375:
1372:
1369:
1366:
1360:
1357:
1354:
1351:
1345:
1318:
1314:
1307:
1302:
1298:
1292:
1288:
1284:
1276:
1272:
1265:
1259:
1256:
1253:
1250:
1247:
1244:
1241:
1238:
1235:
1229:
1204:
1196:
1183:
1170:
1165:
1162:
1159:
1155:
1149:
1146:
1141:
1136:
1132:
1125:
1116:
1115:
1102:
1094:
1092:
1082:
1073:
1070:
1069:
1068:
1067:
1063:
1060:
1057:
1054:
1047:
1046:
1045:
1041:
1040:
1036:
1032:
1011:
1007:
1000:
997:
994:
991:
988:
985:
982:
979:
976:
968:
964:
957:
951:
918:
914:
907:
904:
901:
898:
895:
892:
889:
886:
883:
875:
871:
864:
858:
825:
821:
814:
811:
808:
805:
802:
799:
796:
793:
790:
782:
778:
771:
765:
750:
732:
721:
710:
695:
678:
672:
669:
663:
657:
651:
645:
642:
636:
599:
593:
586:
583:
566:
562:
536:
532:
525:
518:
500:
492:
488:
480:
462:
456:
449:
448:
447:
444:
427:
421:
418:
412:
404:
400:
391:
387:
380:
375:
370:
367:
364:
360:
356:
350:
344:
333:
329:
319:
312:
311:
306:
302:
295:
294:
293:
286:
285:
284:
277:
276:
275:
273:
263:
259:
256:
255:Communication
249:
248:
247:
239:
235:
233:
232:
231:Sonar systems
226:
225:
224:Radar systems
215:
214:
213:
204:
198:Sensors array
196:
192:
190:
186:
181:
177:
173:
169:
164:
155:
152:
148:
144:
141:
140:
139:
136:
134:
133:training data
130:
126:
122:
118:
114:
110:
106:
105:radio antenna
102:
98:
94:
84:
81:
73:
70:November 2012
63:
59:
53:
52:
46:
41:
32:
31:
26:
22:
7085:. Retrieved
7078:the original
7065:
7049:
7040:
6987:
6983:
6977:
6942:
6938:
6932:
6907:
6903:
6893:
6877:
6872:
6829:
6825:
6815:
6805:
6797:
6769:. Retrieved
6765:the original
6755:
6743:. Retrieved
6739:the original
6729:
6721:
6689:
6686:Peter Stoica
6661:
6657:Peter Stoica
6623:
6620:Peter Stoica
6613:
6549:Phased array
6537:
6533:
6435:
6228:
6203:
6128:
5915:
5907:
5800:
5797:
5601:
5576:
5468:
5310:
5307:
5211:
5061:
4965:
4940:
4924:
4840:
4839:in equation
4802:
4791:
4632:
4621:
4460:
4449:
4440:
2947:
2946:
2942:
2933:
2924:
1630:
1629:
1628:
1618:
1608:
1600:
1113:
1112:
1108:
1100:
1090:
1088:
1079:
1042:
1038:
1034:
1033:
751:
696:
618:
445:
331:
327:
325:
316:
299:
290:
281:
268:
253:
244:
241:Radar System
229:
222:
219:
210:
207:Applications
201:
168:sensor array
159:
137:
92:
91:
76:
67:
48:
6604:Torlak, M.
6559:Periodogram
272:beamforming
113:microphones
62:introducing
7118:Categories
7087:8 December
6771:2012-08-06
6735:"About Us"
6585:References
1064:Far-Field.
121:telescopes
45:references
7068:: 67–94.
6839:0809.2266
6514:α
6483:σ
6479:≈
6467:α
6463:−
6460:α
6445:λ
6413:α
6409:−
6406:α
6391:λ
6385:†
6358:−
6342:†
6315:α
6312:−
6291:†
6264:α
6261:−
6250:≈
6244:~
6188:†
6162:σ
6158:−
6144:~
6086:λ
6054:σ
6050:−
6041:λ
6037:≈
6023:σ
6000:†
5989:Λ
5874:−
5866:⋅
5836:−
5828:⋅
5816:~
5772:−
5748:σ
5739:†
5713:σ
5689:−
5665:σ
5656:†
5630:σ
5617:~
5511:⊥
5453:⊥
5427:σ
5418:⊥
5389:⊥
5369:⊥
5347:⊥
5326:~
5292:†
5277:−
5262:†
5244:−
5231:⊥
5195:⊥
5163:†
5132:σ
5100:σ
5032:σ
5023:†
4997:σ
4866:τ
4767:τ
4715:τ
4677:τ
4654:τ
4605:τ
4591:τ
4585:π
4576:
4567:τ
4549:∞
4544:∞
4541:−
4537:∫
4409:θ
4394:−
4372:θ
4363:∗
4338:θ
4323:−
4188:θ
4173:−
4158:∗
4144:θ
4131:μ
4063:θ
4048:−
4033:∗
4019:θ
4009:μ
3984:θ
3975:∗
3899:θ
3884:−
3871:μ
3831:θ
3821:μ
3658:⇔
3636:θ
3627:∗
3616:μ
3585:∗
3542:θ
3533:∗
3414:θ
3405:∗
3245:∗
3202:θ
3193:∗
3074:θ
3065:∗
2824:∗
2796:∗
2773:−
2762:⊥
2653:∞
2641:θ
2610:θ
2569:θ
2558:⊥
2504:θ
2293:θ
2282:⊥
2252:θ
2189:ϵ
2180:θ
1966:∗
1937:λ
1916:∑
1900:σ
1891:∗
1542:θ
1293:∗
1197:∗
1156:∑
722:θ
652:θ
563:θ
533:θ
388:θ
361:∑
189:waveforms
7022:50311217
6882:Archived
6864:14152210
6543:See also
6077:, where
4241:′
1476:′
1050:q < r
180:wireless
7124:Sensors
7033:Sources
7002:Bibcode
6969:4671806
6912:Bibcode
6844:Bibcode
6530:Summary
446:Where:
101:sensors
58:improve
7020:
6967:
6862:
6745:6 June
6684:J Li,
6618:J Li,
6436:where
5916:Since
5469:Since
5062:where
4248:
4222:
3933:
3855:
3846:
3758:
3749:
3737:
3689:
3572:
3444:
3346:
3316:
3304:
3292:
3232:
3104:
3000:
2991:
2978:
2963:
2717:
2708:
2696:
2678:
2601:
2592:
2522:
2507:
2501:
2474:
2462:
2450:
2429:
2383:
2350:
2344:
2335:
2320:
2302:
2267:
2258:
2231:
2222:
2186:
2171:
2153:
2135:
1993:
1790:
1757:
1724:
1715:
1673:
1646:
1599:Where
1554:
1538:
1508:
1464:
1437:
1425:
1413:
1391:
1382:
1364:
1349:
1263:
1233:
1129:
149:) or "
47:, but
7081:(PDF)
7062:(PDF)
7018:S2CID
6992:arXiv
6965:S2CID
6947:arXiv
6860:S2CID
6834:arXiv
6810:1988.
6666:(PDF)
4842:Eq.II
176:sonar
172:radar
7089:2010
6747:2013
6579:SAMV
119:and
107:and
7070:doi
7010:doi
6988:131
6957:doi
6920:doi
6852:doi
6830:120
4689:is
4573:cos
191:.
147:SNR
23:or
7120::
7064:.
7016:.
7008:.
7000:.
6986:.
6963:.
6955:.
6943:46
6941:.
6918:.
6906:.
6902:.
6858:.
6850:.
6842:.
6828:.
6780:^
6698:^
6674:^
6632:^
6593:^
6226::
4917:.
4894:XY
4858:XY
4794:II
4707:XX
4646:XX
4559:XX
4519:XX
4478:XX
4219:5.
3930:4.
3686:3.
3289:2.
2960:1.
2675:5.
2426:4.
2132:3.
1990:2.
1643:1.
1601:Rx
1505:4.
1346:3.
1230:2.
1126:1.
581:),
174:,
115:,
7091:.
7072::
7024:.
7012::
7004::
6994::
6971:.
6959::
6949::
6926:.
6922::
6914::
6908:9
6866:.
6854::
6846::
6836::
6774:.
6749:.
6492:2
6487:s
6476:)
6471:2
6457:2
6454:(
6449:1
6422:)
6417:2
6403:2
6400:(
6395:1
6380:1
6375:u
6368:1
6363:u
6354:R
6350:=
6347:)
6337:1
6332:u
6325:1
6320:u
6308:I
6304:(
6300:R
6296:)
6286:1
6281:u
6274:1
6269:u
6257:I
6253:(
6240:R
6213:R
6183:a
6177:a
6171:2
6166:s
6154:R
6150:=
6140:R
6113:R
6090:1
6063:2
6058:n
6045:1
6032:2
6027:s
5995:U
5984:U
5980:=
5976:R
5953:1
5948:u
5925:a
5893:I
5889:+
5882:2
5879:1
5870:)
5863:(
5858:v
5853:R
5844:2
5841:1
5832:)
5825:(
5822:=
5812:R
5780:2
5777:1
5768:)
5763:I
5757:2
5752:n
5744:+
5734:a
5728:a
5722:2
5717:s
5709:(
5705:R
5697:2
5694:1
5685:)
5680:I
5674:2
5669:n
5661:+
5651:a
5645:a
5639:2
5634:s
5626:(
5623:=
5613:R
5586:R
5556:a
5534:R
5506:a
5501:P
5478:a
5448:a
5443:P
5436:2
5431:n
5423:+
5413:a
5408:P
5401:v
5396:R
5384:a
5379:P
5374:=
5364:a
5359:P
5353:R
5342:a
5337:P
5332:=
5322:R
5287:a
5280:1
5273:)
5268:a
5257:a
5252:(
5248:a
5240:I
5236:=
5226:a
5221:P
5190:a
5185:P
5141:2
5136:n
5109:2
5104:s
5077:v
5072:R
5047:I
5041:2
5036:n
5028:+
5018:a
5012:a
5006:2
5001:s
4993:+
4988:v
4983:R
4978:=
4974:R
4950:a
4905:)
4902:f
4899:(
4890:S
4869:)
4863:(
4854:R
4827:)
4824:t
4821:(
4816:Y
4812:V
4796:)
4792:(
4774:)
4770:)
4764:+
4761:t
4758:(
4753:X
4749:V
4745:)
4742:t
4739:(
4734:X
4730:V
4725:(
4721:=
4718:)
4712:(
4703:R
4657:)
4651:(
4642:R
4626:)
4624:I
4622:(
4601:d
4597:,
4594:)
4588:f
4582:2
4579:(
4570:)
4564:(
4555:R
4533:=
4530:)
4527:f
4524:(
4515:S
4489:)
4486:f
4483:(
4474:S
4456:O
4421:)
4418:)
4413:k
4405:(
4402:a
4397:1
4389:x
4385:R
4381:)
4376:k
4368:(
4359:a
4355:(
4351:/
4347:)
4342:k
4334:(
4331:a
4326:1
4318:x
4314:R
4310:=
4305:k
4301:W
4278:r
4275:e
4272:m
4269:r
4266:o
4263:f
4260:m
4257:a
4254:e
4251:B
4245:s
4238:n
4234:o
4231:p
4228:a
4225:C
4197:)
4192:k
4184:(
4181:a
4176:1
4168:x
4164:R
4154:)
4148:k
4140:(
4137:a
4134:=
4109:n
4106:e
4103:h
4100:T
4078:1
4075:=
4072:)
4067:k
4059:(
4056:a
4051:1
4043:x
4039:R
4029:)
4023:k
4015:(
4012:a
4006:=
4001:k
3997:W
3993:)
3988:k
3980:(
3971:a
3948:e
3945:c
3942:n
3939:i
3936:s
3908:)
3903:k
3895:(
3892:a
3887:1
3879:x
3875:R
3868:=
3863:k
3859:W
3852:r
3849:o
3843:,
3840:)
3835:k
3827:(
3824:a
3818:=
3813:k
3809:w
3803:x
3799:R
3776:n
3773:i
3770:a
3767:t
3764:b
3761:o
3755:e
3752:w
3746:,
3743:t
3740:i
3734:g
3731:n
3728:i
3725:t
3722:a
3719:i
3716:t
3713:n
3710:e
3707:r
3704:e
3701:f
3698:f
3695:i
3692:D
3664:)
3661:1
3653:k
3649:w
3645:)
3640:k
3632:(
3623:a
3619:(
3613:2
3610:+
3605:k
3601:W
3595:k
3591:R
3580:k
3576:W
3567:)
3564:1
3561:=
3556:k
3552:w
3546:k
3538:(
3529:a
3524:n
3520:i
3517:m
3514:=
3492:}
3487:2
3482:|
3478:)
3475:t
3472:(
3469:X
3464:k
3460:W
3455:|
3450:{
3447:E
3439:)
3436:1
3433:=
3428:k
3424:w
3418:k
3410:(
3401:a
3396:n
3392:i
3389:m
3367::
3364:d
3361:o
3358:h
3355:t
3352:e
3349:m
3343:e
3340:g
3337:n
3334:a
3331:r
3328:g
3325:n
3322:a
3319:l
3313:e
3310:h
3307:t
3301:e
3298:s
3295:U
3265:k
3261:W
3255:k
3251:R
3240:k
3236:W
3227:)
3224:1
3221:=
3216:k
3212:w
3206:k
3198:(
3189:a
3184:n
3180:i
3177:m
3174:=
3152:}
3147:2
3142:|
3138:)
3135:t
3132:(
3129:X
3124:k
3120:W
3115:|
3110:{
3107:E
3099:)
3096:1
3093:=
3088:k
3084:w
3078:k
3070:(
3061:a
3056:n
3052:i
3049:m
3027::
3024:e
3021:z
3018:i
3015:m
3012:i
3009:n
3006:i
3003:m
2997:o
2994:t
2986:K
2982:W
2975:d
2972:n
2969:i
2966:F
2911:]
2906:M
2902:e
2898:,
2895:.
2892:.
2889:.
2886:.
2883:,
2880:1
2877:+
2872:d
2868:e
2864:[
2861:=
2856:n
2852:E
2819:n
2815:E
2809:n
2805:E
2801:=
2791:s
2787:E
2781:s
2777:E
2770:I
2767:=
2757:A
2753:P
2730::
2725:x
2721:R
2714:f
2711:o
2705:D
2702:V
2699:E
2693:r
2690:e
2687:t
2684:f
2681:A
2650:=
2644:)
2638:(
2635:a
2630:A
2626:P
2621:1
2616:=
2613:)
2607:(
2604:M
2598:r
2595:o
2589:0
2586:=
2581:2
2576:|
2572:)
2566:(
2563:a
2552:A
2547:P
2542:|
2537::
2534:t
2531:a
2528:h
2525:t
2519:h
2516:c
2513:u
2510:s
2498:e
2495:l
2492:b
2489:i
2486:s
2483:s
2480:o
2477:p
2471:l
2468:l
2465:a
2459:r
2456:o
2453:f
2447:h
2444:c
2441:r
2438:a
2435:e
2432:S
2404:.
2401:x
2398:i
2395:r
2392:t
2389:a
2386:m
2380:n
2377:o
2374:i
2371:t
2368:c
2365:e
2362:j
2359:o
2356:r
2353:p
2347:a
2341:s
2338:i
2330:A
2325:P
2317:e
2314:r
2311:e
2308:h
2305:w
2299:,
2296:)
2290:(
2287:a
2276:A
2271:P
2264:r
2261:o
2255:)
2249:(
2246:a
2241:A
2236:P
2228:r
2225:o
2219:}
2214:s
2209:E
2204:{
2201:n
2198:a
2195:p
2192:s
2183:)
2177:(
2174:a
2168:h
2165:c
2162:i
2159:h
2156:w
2150:k
2147:c
2144:e
2141:h
2138:C
2110:.
2107:}
2102:s
2097:E
2092:{
2089:n
2086:a
2083:p
2080:s
2077:=
2074:}
2069:d
2065:e
2061:,
2058:.
2055:.
2052:.
2049:.
2046:,
2043:1
2040:e
2037:{
2034:e
2031:n
2028:a
2025:p
2022:s
2019:=
2016:}
2012:A
2008:{
2005:n
2002:a
1999:p
1996:s
1961:k
1957:r
1951:k
1947:e
1941:k
1931:M
1926:1
1923:=
1920:k
1912:=
1909:I
1904:2
1896:+
1886:A
1879:s
1874:R
1868:A
1864:=
1859:x
1855:R
1832::
1829:n
1826:o
1823:i
1820:t
1817:i
1814:s
1811:o
1808:p
1805:m
1802:o
1799:c
1796:e
1793:d
1787:e
1784:u
1781:l
1778:a
1775:v
1772:n
1769:e
1766:g
1763:i
1760:e
1754:g
1751:n
1748:i
1745:m
1742:r
1739:o
1736:f
1733:r
1730:e
1727:p
1721:y
1718:b
1712:n
1709:o
1706:i
1703:t
1700:i
1697:s
1694:o
1691:p
1688:m
1685:o
1682:c
1679:e
1676:d
1670:e
1667:c
1664:a
1661:p
1658:s
1655:b
1652:u
1649:S
1609:F
1584:.
1581:q
1578:.
1575:.
1572:.
1569:.
1566:,
1563:1
1560:=
1557:i
1551:,
1546:k
1535:e
1532:t
1529:a
1526:l
1523:u
1520:c
1517:l
1514:a
1511:C
1483:.
1480:s
1472:i
1468:w
1461:e
1458:l
1455:b
1452:i
1449:s
1446:s
1443:o
1440:p
1434:l
1431:l
1428:a
1422:r
1419:o
1416:f
1410:)
1405:i
1401:W
1397:(
1394:B
1388:f
1385:o
1379:s
1376:k
1373:a
1370:e
1367:P
1361:d
1358:n
1355:i
1352:F
1324:)
1319:i
1315:W
1311:(
1308:F
1303:x
1299:R
1289:F
1285:=
1282:)
1277:i
1273:W
1269:(
1266:B
1260:e
1257:t
1254:a
1251:l
1248:u
1245:c
1242:l
1239:a
1236:C
1208:)
1205:t
1202:(
1192:x
1187:)
1184:t
1181:(
1177:x
1171:M
1166:1
1163:=
1160:t
1150:M
1147:1
1142:=
1137:x
1133:R
1052:.
1020:]
1017:)
1012:M
1008:t
1004:(
1001:s
998:,
995:.
992:.
989:.
986:.
983:.
980:.
977:,
974:)
969:1
965:t
961:(
958:s
955:[
952:=
948:S
927:]
924:)
919:M
915:t
911:(
908:n
905:,
902:.
899:.
896:.
893:.
890:.
887:.
884:,
881:)
876:1
872:t
868:(
865:n
862:[
859:=
855:N
834:]
831:)
826:M
822:t
818:(
815:x
812:,
809:.
806:.
803:.
800:.
797:.
794:.
791:,
788:)
783:1
779:t
775:(
772:x
769:[
766:=
762:X
737:N
733:+
729:S
725:)
719:(
715:A
711:=
707:X
682:)
679:t
676:(
673:n
670:+
667:)
664:t
661:(
658:s
655:)
649:(
646:A
643:=
640:)
637:t
634:(
630:x
603:)
600:t
597:(
594:n
567:k
542:)
537:k
529:(
526:a
504:)
501:t
498:(
493:k
489:s
466:)
463:t
460:(
457:x
431:)
428:t
425:(
422:n
419:+
416:)
413:t
410:(
405:k
401:s
397:)
392:k
384:(
381:a
376:q
371:1
368:=
365:K
357:=
354:)
351:t
348:(
345:x
332:q
328:r
153:"
83:)
77:(
72:)
68:(
54:.
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
