412:
2247:
549:
4348:
5950:
428:
5909:
6146:
4275:
36:
5067:
4680:
4548:—depend on the characteristics of the filter. The term "low-pass filter" merely refers to the shape of the filter's response; a high-pass filter could be built that cuts off at a lower frequency than any low-pass filter—it is their responses that set them apart. Electronic circuits can be devised for any desired frequency range, right up through microwave frequencies (above 1 GHz) and higher.
3266:
4256:
time-domain response of an ideal sharp-cutoff low-pass filter. For minimum distortion, the finite impulse response filter has an unbounded number of coefficients operating on an unbounded signal. In practice, the time-domain response must be time truncated and is often of a simplified shape; in the
4335:
For non-realtime filtering, to achieve a low pass filter, the entire signal is usually taken as a looped signal, the
Fourier transform is taken, filtered in the frequency domain, followed by an inverse Fourier transform. Only O(n log(n)) operations are required compared to O(n) for the time domain
482:
However, the ideal filter is impossible to realize without also having signals of infinite extent in time, and so generally needs to be approximated for real ongoing signals, because the sinc function's support region extends to all past and future times. The filter would therefore need to have
187:
may have different meanings, depending on whether referring to the frequency or wavelength of light, since these variables are inversely related. High-pass frequency filters would act as low-pass wavelength filters, and vice versa. For this reason, it is a good practice to refer to wavelength
3093:
483:
infinite delay, or knowledge of the infinite future and past, to perform the convolution. It is effectively realizable for pre-recorded digital signals by assuming extensions of zero into the past and future, or, more typically, by making the signal repetitive and using
Fourier analysis.
4907:
At high frequencies, the capacitor only has time to charge up a small amount before the input switches direction. The output goes up and down only a small fraction of the amount the input goes up and down. At double the frequency, there's only time for it to charge up half the
3407:
5123:. The presence of the resistance also reduces the peak resonant frequency somewhat. Some resistance is unavoidable in real circuits, even if a resistor is not specifically included as a component. An ideal, pure LC circuit is an abstraction for the purpose of theory.
4481:
reduces the signal amplitude to one-fourth of its original level every time the frequency doubles (so power decreases by 12 dB per octave, or 40 dB per decade). Other all-pole second-order filters may roll off at different rates initially depending on their
2758:
1444:
664:
5381:
467:. The transition region present in practical filters does not exist in an ideal filter. An ideal low-pass filter can be realized mathematically (theoretically) by multiplying a signal by the rectangular function in the frequency domain or, equivalently,
4459:, the Bode plot flattens out again, at some maximum attenuation of high frequencies; such an effect is caused for example by a little bit of the input leaking around the one-pole filter; this one-pole–one-zero filter is still a first-order low-pass.
1130:
277:
A stiff physical barrier tends to reflect higher sound frequencies, acting as an acoustic low-pass filter for transmitting sound. When music is playing in another room, the low notes are easily heard, while the high notes are attenuated.
4707:, and blocks low-frequency signals, forcing them through the load instead. At higher frequencies, the reactance drops, and the capacitor effectively functions as a short circuit. The combination of resistance and capacitance gives the
2646:
246:. That is a filter with unity bandwidth and impedance. The desired filter is obtained from the prototype by scaling for the desired bandwidth and impedance and transforming into the desired bandform (that is, low-pass, high-pass,
517:
involves understanding and minimizing these artifacts. For example, simple truncation of the sinc function will create severe ringing artifacts, which can be reduced using window functions that drop off more smoothly at the edges.
3799:
3261:{\displaystyle y_{i}=\overbrace {x_{i}\left({\frac {\Delta _{T}}{RC+\Delta _{T}}}\right)} ^{\text{Input contribution}}+\overbrace {y_{i-1}\left({\frac {RC}{RC+\Delta _{T}}}\right)} ^{\text{Inertia from previous output}}.}
1620:
4626:
2508:
4564:, in a way that lets all characteristics of the filter be easily analyzed by considering the pattern of poles and zeros of the Laplace transform in the complex plane. (In discrete time, one can similarly consider the
3562:
5118:
will. The main difference that the presence of the resistor makes is that any oscillation induced in the circuit will die away over time if it is not kept going by a source. This effect of the resistor is called
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1993:
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attenuates high frequencies more steeply. The Bode plot for this type of filter resembles that of a first-order filter, except that it falls off more quickly. For example, a second-order
2660:
1237:
5830:- Signals are phase-shifted 180° and attenuated by the square of the frequency ratio. This behavior is detailed by Jim Karki in "Active Low-Pass Filter Design" (Texas Instruments, 2023).
3673:
3450:
569:
5639:
5142:, where they are used to select a narrow range of frequencies from the ambient radio waves. In this role, the circuit is often called a tuned circuit. An RLC circuit can be used as a
3619:
5234:
4447:, and a diagonal line above the cutoff frequency. There is also a "knee curve" at the boundary between the two, smoothly transitioning between the two straight-line regions. If the
1669:
873:
1731:
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239:
techniques as are used for other low-pass filters. Low-pass filters provide a smoother form of a signal, removing the short-term fluctuations and leaving the longer-term trend.
5564:
4957:
3917:
1494:
498:; applying that filter requires delaying the signal for a moderate period of time, allowing the computation to "see" a little bit into the future. This delay is manifested as
708:
2910:
2198:
5690:
4385:
2815:
4740:
4486:, but approach the same final rate of 12 dB per octave; as with the first-order filters, zeroes in the transfer function can change the high-frequency asymptote. See
3490:
2788:
1828:
423:
of an ideal low-pass filter. The ripples of a true sinc extend infinitely to the left and right while getting smaller and smaller, but this particular graph is truncated.
5745:
5519:
5207:
4399:
There are many different types of filter circuits, with different responses to changing frequency. The frequency response of a filter is generally represented using a
1209:
2560:
5895:
5463:
4096:
5485:
is the quality factor. Equation 1 describes three regions of operation: below cutoff, in the area of cutoff, and above cutoff. For each area, Equation 1 reduces to:
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5862:
5430:
3707:
735:
1001:
1165:
5710:
5584:
5483:
5403:
5227:
4974:
The capacitor is not an "on/off" object (like the block or pass fluidic explanation above). The capacitor variably acts between these two extremes. It is the
2168:
1229:
2581:
4339:
This can also sometimes be done in real time, where the signal is delayed long enough to perform the
Fourier transformation on shorter, overlapping blocks.
2239:
The effect of an infinite impulse response low-pass filter can be simulated on a computer by analyzing an RC filter's behavior in the time domain, and then
6414:
for digital implementation of
Butterworth, Bessel, and Chebyshev filters created by the late Dr. Tony Fisher of the University of York (York, England).
3715:
3967:
The filter recurrence relation provides a way to determine the output samples in terms of the input samples and the preceding output. The following
2763:
This equation can be discretized. For simplicity, assume that samples of the input and output are taken at evenly spaced points in time separated by
6343:
6314:
4966:(AC) flows very well through the capacitor, almost as well as it flows through a solid wire, AC input flows out through the capacitor, effectively
1502:
4577:
2079:, we find that there is an exact reconstruction (0% error). This is the reconstructed output for a time-invariant input. However, if the input is
2448:
3502:
4756:
5958:
6439:
6182:
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4840:
522:
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886:
743:
1998:
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At low frequencies, there is plenty of time for the capacitor to charge up to practically the same voltage as the input voltage.
3402:{\displaystyle y_{i}=\alpha x_{i}+(1-\alpha )y_{i-1}\qquad {\text{where}}\qquad \alpha :={\frac {\Delta _{T}}{RC+\Delta _{T}}}.}
2273:
5094:, connected in series or in parallel. The RLC part of the name is due to those letters being the usual electrical symbols for
100:
5050:
6064:
883:
The most common way to characterize the frequency response of a circuit is to find its
Laplace transform transfer function,
72:
6401:
6000:
5042:
2086:
296:
for voltage signals, high frequencies in the input signal are attenuated, but the filter has little attenuation below the
1921:
1836:
4900:
This circuit may be understood by considering the time the capacitor needs to charge or discharge through the resistor:
4509:
On any
Butterworth filter, if one extends the horizontal line to the right and the diagonal line to the upper-left (the
4443:
in the limit of high frequency. The magnitude Bode plot for a first-order filter looks like a horizontal line below the
6524:
4169:
4101:
2915:
2820:
530:
79:
5864:
increasing by a power of two, the last formula describes a second-order low-pass filter. The frequency scaling factor
3926:
6364:
6223:
4322:
2753:{\displaystyle v_{\text{in}}(t)-v_{\text{out}}(t)=RC{\frac {\operatorname {d} v_{\text{out}}}{\operatorname {d} t}}.}
1439:{\displaystyle v_{\rm {out}}(nT)-v_{\rm {out}}((n-1)T)=V_{i}(1-e^{-\omega _{0}nT})-V_{i}(1-e^{-\omega _{0}((n-1)T)})}
119:
4304:
659:{\displaystyle v_{\text{out}}(t)=v_{\text{in}}(t)-RC{\frac {\operatorname {d} v_{\text{out}}}{\operatorname {d} t}}}
6432:
4296:
2368:
340:
235:
operation used in fields such as finance is a particular kind of low-pass filter and can be analyzed with the same
53:
5376:{\displaystyle H_{LP}(f)=-{\frac {K}{f_{FSF}\cdot f_{c}^{2}+{\frac {1}{Q}}\cdot jf_{FSF}\cdot f_{c}+1}}\quad (1)}
4493:
Third- and higher-order filters are defined similarly. In general, the final rate of power rolloff for an order-
3624:
3419:
373:
Low-pass filters also play a significant role in the sculpting of sound created by analogue and virtual analogue
327:, to block high pitches that they cannot efficiently reproduce. Radio transmitters use low-pass filters to block
141:
86:
5591:
5020:. A first-order RL circuit is composed of one resistor and one inductor and is the simplest type of RL circuit.
4423:
of the filter determines the amount of additional attenuation for frequencies higher than the cutoff frequency.
3573:
6404:, an intuitive explanation of the source of phase shift in a low-pass filter. Also verifies simple passive LPF
6395:
4300:
57:
6390:
6284:
1628:
833:
4060:
1676:
1736:
68:
6519:
400:
392:
220:
545:
The time response of a low-pass filter is found by solving the response to the simple low-pass RC filter.
6425:
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560:
534:
355:
5524:
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3894:
6509:
6448:
1452:
1141:
305:
137:
677:
5897:
is used to scale the cutoff frequency of the filter so that it follows the definitions given before.
5027:
4241:
2220:
2888:
2177:
6134:
drops off at −6 dB per octave (that is −20 dB per decade) as it is a first-order filter.
5644:
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4285:
2793:
232:
4714:
6514:
4913:
4704:
4456:
4452:
4289:
3468:
2766:
2224:
1793:
495:
351:
285:
with the same function can correctly be called a low-pass filter, but conventionally is called a
46:
17:
5717:
5491:
6215:
6208:
5173:
5158:
circuit, meaning that any voltage or current in the circuit can be described by a second-order
4696:
1170:
1125:{\displaystyle H(s)={V_{\rm {out}}(s) \over V_{\rm {in}}(s)}={\omega _{0} \over s+\omega _{0}}}
514:
6239:
5905:
Higher-order passive filters can also be constructed (see diagram for a third-order example).
2529:
5987:
5867:
5435:
5159:
5127:
5095:
4081:
4064:
3276:
396:
380:
93:
5840:
5408:
4534:
4431:, for example, reduces the signal amplitude by half (so power reduces by a factor of 4, or
4068:
3685:
1231:
is the time between samples. Taking the difference between two consecutive samples we have
713:
460:
388:
216:
977:
8:
5131:
5107:
4963:
3085:
2641:{\displaystyle i(t)\;=\;C{\frac {\operatorname {d} v_{\text{out}}}{\operatorname {d} t}}}
487:
5126:
There are many applications for this circuit. They are used in many different types of
1147:
207:
Low-pass filters exist in many different forms, including electronic circuits such as a
6529:
6337:
6308:
6151:
5980:
5695:
5569:
5468:
5388:
5212:
5079:
4979:
4688:
4648:
4518:
4478:
4462:
4440:
2209:
2153:
2150:, this model approximates the input signal as a series of step functions with duration
1214:
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157:
4991:
4674:
6490:
6405:
6360:
6264:
6219:
5962:
5030:
4557:
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2228:
1144:
is easily obtained by sampling the step input response above at regular intervals of
526:
506:
464:
440:
236:
4571:
For example, a first-order low-pass filter can be described in
Laplace notation as:
3971:
algorithm simulates the effect of a low-pass filter on a series of digital samples:
6479:
6474:
6464:
5917:
5151:
5147:
5143:
5135:
5001:
4747:
4561:
4545:
4522:
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4404:
4352:
4039:
4031:
3974:// Return RC low-pass filter output samples, given input samples, // time interval
510:
472:
452:
431:
The gain-magnitude frequency response of a first-order (one-pole) low-pass filter.
420:
359:
301:
297:
251:
247:
243:
173:
149:
6375:
6469:
4746:). The break frequency, also called the turnover frequency, corner frequency, or
4258:
2240:
491:
332:
309:
212:
3794:{\displaystyle \alpha ={\frac {2\pi \Delta _{T}f_{c}}{2\pi \Delta _{T}f_{c}+1}}}
331:
emissions that might interfere with other communications. The tone knob on many
6534:
5913:
5139:
5046:
5017:
5013:
4924:(DC) cannot flow through the capacitor, DC input must flow out the path marked
4921:
2980:, which correspond to the same points in time. Making these substitutions,
2216:
2170:
producing an error in the reconstructed output signal. The error produced from
282:
224:
5209:
of a second-order low-pass filter can be expressed as a function of frequency
2246:
548:
6503:
5976:
5972:
5024:
4967:
4708:
4640:
4526:
4351:
Plot of the gain of
Butterworth low-pass filters of orders 1 through 5, with
4253:
4072:
3457:
1615:{\displaystyle v_{\rm {out}}(nT)=\beta v_{\rm {out}}((n-1)T)+(1-\beta )V_{i}}
499:
476:
416:
411:
228:
161:
6417:
4621:{\displaystyle {\frac {\text{Output}}{\text{Input}}}=K{\frac {1}{\tau s+1}}}
4347:
974:. Taking the Laplace transform of our differential equation and solving for
304:. For current signals, a similar circuit, using a resistor and capacitor in
5949:
2503:{\displaystyle i(t)={\frac {\operatorname {d} Q_{c}}{\operatorname {d} t}}}
363:
347:
6398:, a short primer on the mathematical analysis of (electrical) LTI systems.
6298:
335:
is a low-pass filter used to reduce the amount of treble in the sound. An
5103:
5075:
4565:
4487:
2262:
468:
448:
374:
324:
271:
6411:
5229:
as shown in
Equation 1, the Second-Order Low-Pass Filter Standard Form.
3557:{\displaystyle RC=\Delta _{T}\left({\frac {1-\alpha }{\alpha }}\right).}
2208:
For another method of conversion from continuous- to discrete-time, see
1918:
Comparing the reconstructed output signal from the difference equation,
513:, which can be reduced or worsened by the choice of windowing function.
6203:
5115:
5099:
4820:{\displaystyle f_{\mathrm {c} }={1 \over 2\pi \tau }={1 \over 2\pi RC}}
4466:
4063:
to the difference between the previous output and the next input. This
3968:
2251:
553:
427:
336:
4970:
to the ground (analogous to replacing the capacitor with just a wire).
4517:, 3 dB below the horizontal line. The various types of filters (
5908:
5111:
5091:
4997:
4975:
4700:
4510:
4416:
4400:
3873:{\displaystyle f_{c}={\frac {\alpha }{(1-\alpha )2\pi \Delta _{T}}}.}
3074:{\displaystyle x_{i}-y_{i}=RC\,{\frac {y_{i}-y_{i-1}}{\Delta _{T}}}.}
1135:
320:
293:
263:
156:
signals with frequencies higher than the cutoff frequency. The exact
153:
145:
4274:
35:
6327:
6159:
6145:
6131:
5692:- Signals are phase-shifted 90° and modified by the quality factor
5087:
5083:
5038:
5034:
5009:
5005:
4890:{\displaystyle \omega _{\mathrm {c} }={1 \over \tau }={1 \over RC}}
4692:
4652:
4483:
4408:
328:
4252:
Finite-impulse-response filters can be built that approximate the
5823:{\displaystyle H_{LP}(f)\approx -{\frac {K}{f_{FSF}\cdot f^{2}}}}
5120:
4912:
Another way to understand this circuit is through the concept of
4236:
436:
6303:. New York: McGRAW-HILL BOOK COMPANY. pp. 211–224, 684–729.
525:
describes how to use a perfect low-pass filter to reconstruct a
172:
in audio applications. A low-pass filter is the complement of a
5078:(the letters R, L, and C can be in a different sequence) is an
5066:
4831:
4439:); more precisely, the power rolloff approaches 20 dB per
4436:
443:
is shown on a logarithmic scale in units of radians per second.
289:
filter (low frequency is long wavelength), to avoid confusion.
267:
5959:
operational amplifier applications § Inverting integrator
4556:
Continuous-time filters can also be described in terms of the
4071:
decay seen in the continuous-time system. As expected, as the
502:. Greater accuracy in approximation requires a longer delay.
6330:
Elementary
Differential Equations and Boundary Value Problems
5991:
5165:
4679:
967:{\displaystyle H(s)={V_{\rm {out}}(s) \over V_{\rm {in}}(s)}}
820:{\displaystyle v_{\text{out}}(t)=V_{i}(1-e^{-\omega _{0}t}),}
2072:{\displaystyle v_{\text{out}}(t)=V_{i}(1-e^{-\omega _{0}t})}
490:
applications approximate the ideal filter by truncating and
5566:- The circuit passes signals multiplied by the gain factor
4059:
That is, the change from one filter output to the next is
2340:{\displaystyle v_{\text{in}}(t)-v_{\text{out}}(t)=R\;i(t)}
2234:
6358:
Signal recovery from noise in electronic instrumentation.
4743:
6376:
Active Low-Pass Filter Design" (Texas Instruments, 2023)
3923:
is significantly larger than the sampling interval, and
439:
decline reflects an additional half-power attenuation).
3271:
That is, this discrete-time implementation of a simple
242:
Filter designers will often use the low-pass form as a
6106:{\displaystyle \omega _{\text{c}}={\frac {1}{R_{2}C}}}
5990:
circuit shown in the figure, the cutoff frequency (in
6067:
6048:{\displaystyle f_{\text{c}}={\frac {1}{2\pi R_{2}C}}}
6003:
5870:
5843:
5753:
5720:
5698:
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5594:
5572:
5527:
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respond more slowly to a change in the input samples
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680:
572:
6184:
Long Pass Filters and Short Pass Filters Information
6141:
2257:
From the circuit diagram to the right, according to
2219:
are designed to give low-pass characteristics. Both
2143:{\displaystyle v_{\text{in}}(t)=V_{i}\sin(\omega t)}
6299:Hayt, William H. Jr. and Kemmerly, Jack E. (1978).
1988:{\displaystyle V_{n}=\beta V_{n-1}+(1-\beta )v_{n}}
1903:{\displaystyle V_{n}=\beta V_{n-1}+(1-\beta )v_{n}}
60:. Unsourced material may be challenged and removed.
6332:. New York: JOHN WILEY & SONS. pp. 11–24.
6207:
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4703:in parallel with the load. The capacitor exhibits
4620:
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1136:Difference equation through discrete time sampling
1124:
995:
966:
867:
819:
729:
702:
658:
319:Electronic low-pass filters are used on inputs to
4227:{\displaystyle (x_{1},\,x_{2},\,\ldots ,\,x_{n})}
4159:{\displaystyle (y_{1},\,y_{2},\,\ldots ,\,y_{n})}
4078:increases, the discrete-time smoothing parameter
4011:α := dt / (RC + dt) y := α * x
2973:{\displaystyle (y_{1},\,y_{2},\,\ldots ,\,y_{n})}
2878:{\displaystyle (x_{1},\,x_{2},\,\ldots ,\,x_{n})}
2174:inputs is difficult to quantify but decreases as
6501:
6177:
6175:
5944:
5916:). The filter becomes a Butterworth filter with
5023:A first-order RL circuit is one of the simplest
4750:(in hertz), is determined by the time constant:
4513:of the function), they intersect at exactly the
4435:, every time the frequency doubles (goes up one
3957:{\displaystyle \Delta _{T}\;\approx \;\alpha RC}
737:then the differential equation has the solution
451:completely eliminates all frequencies above the
313:
5900:
4533:. Many second-order filters have "peaking" or
2562:is the charge stored in the capacitor at time
227:for smoothing sets of data, acoustic barriers,
4658:
4544:The meanings of 'low' and 'high'—that is, the
4342:
669:
505:Truncating an ideal low-pass filter result in
196:to avoid confusion, which would correspond to
6447:
6433:
6172:
4419:the input power by half or 3 dB. So the
3891:time constant equals the sampling period. If
2420:{\displaystyle Q_{c}(t)=C\,v_{\text{out}}(t)}
6342:: CS1 maint: multiple names: authors list (
6328:Boyce, William and DiPrima, Richard (1965).
6313:: CS1 maint: multiple names: authors list (
4261:can be used, giving a square time response.
2203:
6285:Mastering Windows: Improving Reconstruction
4303:. Unsourced material may be challenged and
3668:{\displaystyle RC={\frac {1}{2\pi f_{c}}},}
3445:{\displaystyle 0\;\leq \;\alpha \;\leq \;1}
2227:low pass filters, as well as filters using
6440:
6426:
6396:ECE 209: Review of Circuits as LTI Systems
6263:. Pcweenie.com. 2009-04-12. Archived from
6202:
5634:{\displaystyle {\frac {f}{f_{c}}}=f_{FSF}}
5166:Second-Order Low-Pass Filter Standard Form
4725:
4721:
4247:
4023:n y := α * x + (1-α) * y
3944:
3940:
3905:
3901:
3614:{\displaystyle f_{c}={\frac {1}{2\pi RC}}}
3438:
3434:
3430:
3426:
2601:
2597:
2324:
6058:or equivalently (in radians per second):
4403:, and the filter is characterized by its
4323:Learn how and when to remove this message
4210:
4203:
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4142:
4135:
4121:
3022:
2956:
2949:
2935:
2861:
2854:
2840:
2648:, which can be substituted into equation
2397:
455:while passing those below unchanged; its
406:
120:Learn how and when to remove this message
5948:
5907:
5130:. Another important application is for
5065:
4678:
4346:
2245:
1664:{\displaystyle \beta =e^{-\omega _{0}T}}
868:{\displaystyle \omega _{0}={1 \over RC}}
547:
494:the infinite impulse response to make a
426:
410:
6214:. Saunders College Publishing. p.
4683:Passive, first order low-pass RC filter
4451:of a first-order low-pass filter has a
2235:Simple infinite impulse response filter
1726:{\displaystyle V_{n}=v_{\rm {out}}(nT)}
875:is the cutoff frequency of the filter.
563:we arrive at the differential equation
523:Whittaker–Shannon interpolation formula
14:
6502:
6261:"Home Networking – Local Area Network"
5837:With attenuation at frequencies above
4959:(analogous to removing the capacitor).
1790:, and substituting our sampled value,
1783:{\displaystyle v_{n}=v_{\rm {in}}(nT)}
262:Examples of low-pass filters occur in
6421:
5465:is the frequency scaling factor, and
5106:, respectively. The circuit forms a
3277:exponentially weighted moving average
878:
6294:
6292:
4301:adding citations to reliable sources
4268:
4264:
4056:n y := y + α * (x - y)
2442:
2362:
2267:
58:adding citations to reliable sources
29:
6408:by means of trigonometric identity.
5154:. The RLC filter is described as a
4635:is the Laplace transform variable,
4551:
4537:that puts their frequency response
4529:, etc.) all have different-looking
4244:(IIR) single-pole low-pass filter.
308:, works in a similar manner. (See
164:. The filter is sometimes called a
24:
5559:{\displaystyle H_{LP}(f)\approx K}
4952:{\displaystyle V_{\mathrm {out} }}
4943:
4940:
4937:
4850:
4766:
4541:the horizontal line at this peak.
4098:decreases, and the output samples
3931:
3912:{\displaystyle \alpha \;\ll \;0.5}
3855:
3763:
3735:
3516:
3473:
3384:
3364:
3227:
3151:
3131:
3057:
2771:
2735:
2717:
2626:
2608:
2488:
2470:
1762:
1759:
1705:
1702:
1699:
1554:
1551:
1548:
1518:
1515:
1512:
1468:
1465:
1462:
1286:
1283:
1280:
1253:
1250:
1247:
1069:
1066:
1043:
1040:
1037:
946:
943:
920:
917:
914:
644:
626:
362:vice versa), which share the same
25:
6546:
6384:
6289:
4742:(represented by the Greek letter
1913:
1830:, we get the difference equation
1489:{\displaystyle v_{\rm {out}}(nT)}
537:uses real filter approximations.
515:Design and choice of real filters
350:use low-pass filters to separate
6144:
5070:RLC circuit as a low-pass filter
4992:RL circuit § Series circuit
4675:RC circuit § Series circuit
4273:
3465:in terms of the sampling period
710:be a step function of magnitude
703:{\displaystyle v_{\text{in}}(t)}
540:
435:is shown in decibels (i.e., a 3
387:A low-pass filter is used as an
219:for conditioning signals before
34:
6402:ECE 209: Sources of Phase Shift
5912:A third-order low-pass filter (
5363:
5056:
4996:A resistor–inductor circuit or
3354:
3348:
2912:be represented by the sequence
2817:be represented by the sequence
45:needs additional citations for
6391:Low Pass Filter java simulator
6369:
6350:
6321:
6278:
6253:
6232:
6210:Microelectronic Circuits, 3 ed
6196:
5773:
5767:
5667:
5661:
5547:
5541:
5370:
5364:
5257:
5251:
5196:
5190:
4663:
4221:
4173:
4153:
4105:
3845:
3833:
3329:
3317:
2967:
2919:
2905:{\displaystyle v_{\text{out}}}
2872:
2824:
2702:
2696:
2680:
2674:
2594:
2588:
2549:
2543:
2461:
2455:
2414:
2408:
2388:
2382:
2334:
2328:
2315:
2309:
2293:
2287:
2193:{\displaystyle T\rightarrow 0}
2184:
2137:
2128:
2106:
2100:
2066:
2034:
2018:
2012:
1995:, to the step input response,
1972:
1960:
1887:
1875:
1777:
1768:
1720:
1711:
1599:
1587:
1581:
1575:
1563:
1560:
1533:
1524:
1483:
1474:
1433:
1428:
1422:
1410:
1407:
1380:
1364:
1329:
1313:
1307:
1295:
1292:
1268:
1259:
1081:
1075:
1055:
1049:
1022:
1016:
990:
984:
958:
952:
932:
926:
899:
893:
811:
779:
763:
757:
697:
691:
611:
605:
589:
583:
13:
1:
6165:
6116:The gain in the passband is −
5945:Active electronic realization
5685:{\displaystyle H_{LP}(f)=jKQ}
5061:
4380:{\displaystyle \omega _{0}=1}
2810:{\displaystyle v_{\text{in}}}
160:of the filter depends on the
6301:Engineering Circuit Analysis
6206:; Smith, Kenneth C. (1991).
5901:Higher order passive filters
5053:driven by a current source.
4985:
4982:that show this variability.
4735:{\displaystyle \tau \;=\;RC}
4668:
4034:that calculates each of the
3251:Inertia from previous output
3084:Rearranging terms gives the
535:digital-to-analog converters
401:digital-to-analog conversion
346:Telephone lines fitted with
221:analog-to-digital conversion
7:
6137:
5405:is the frequency variable,
4916:at a particular frequency:
4687:One simple low-pass filter
4659:Electronic low-pass filters
4387:. Note that the slope is 20
4343:Continuous-time realization
3485:{\displaystyle \Delta _{T}}
2783:{\displaystyle \Delta _{T}}
2650:
2574:
2568:
2516:
2433:
2353:
1823:{\displaystyle v_{n}=V_{i}}
670:Step input response example
257:
10:
6551:
5956:
5740:{\displaystyle f\gg f_{c}}
5514:{\displaystyle f\ll f_{c}}
4989:
4672:
4568:of the impulse response.)
2207:
292:In an electronic low-pass
231:of images, and so on. The
6525:Filter frequency response
6488:
6455:
6449:Signal-processing filters
5953:An active low-pass filter
5432:is the cutoff frequency,
5202:{\displaystyle H_{LP}(f)}
5028:infinite impulse response
4242:infinite-impulse-response
2790:time. Let the samples of
2221:infinite impulse response
2204:Discrete-time realization
1204:{\displaystyle n=0,1,...}
312:discussed in more detail
6356:Whilmshurst, T H (1990)
6240:"ADSL filters explained"
5971:low-pass filter adds an
2566:. Substituting equation
2555:{\displaystyle Q_{c}(t)}
5924:=1 when (for example) C
5890:{\displaystyle f_{FSF}}
5458:{\displaystyle f_{FSF}}
5114:in a similar way as an
4411:. In all cases, at the
4248:Finite impulse response
4091:{\displaystyle \alpha }
3452:. The expression for
3275:low-pass filter is the
2225:finite impulse response
496:finite impulse response
6465:High-pass filter (HPF)
6107:
6049:
5954:
5941:
5891:
5858:
5824:
5741:
5706:
5686:
5635:
5580:
5560:
5515:
5479:
5459:
5426:
5399:
5377:
5223:
5203:
5170:The transfer function
5150:, low-pass filter, or
5071:
4953:
4891:
4821:
4736:
4684:
4622:
4407:and rate of frequency
4396:
4381:
4234:; the system has more
4228:
4160:
4092:
3958:
3913:
3874:
3795:
3703:
3669:
3615:
3558:
3492:and smoothing factor
3486:
3456:yields the equivalent
3446:
3403:
3262:
3075:
2974:
2906:
2879:
2811:
2784:
2754:
2642:
2556:
2504:
2421:
2341:
2261:and the definition of
2254:
2194:
2164:
2144:
2073:
1989:
1904:
1824:
1784:
1727:
1665:
1616:
1490:
1440:
1225:
1205:
1161:
1126:
997:
968:
869:
821:
731:
704:
660:
556:
479:, in the time domain.
444:
424:
407:Ideal and real filters
148:lower than a selected
6460:Low-pass filter (LPF)
6108:
6050:
5988:operational amplifier
5952:
5911:
5892:
5859:
5857:{\displaystyle f_{c}}
5825:
5742:
5707:
5687:
5636:
5581:
5561:
5516:
5480:
5460:
5427:
5425:{\displaystyle f_{c}}
5400:
5378:
5224:
5204:
5162:in circuit analysis.
5160:differential equation
5110:for current and will
5069:
4954:
4892:
4822:
4737:
4682:
4651:of the filter in the
4623:
4382:
4350:
4336:filtering algorithm.
4240:. This filter is an
4229:
4161:
4093:
4067:property matches the
4065:exponential smoothing
4042:into the equivalent:
3959:
3914:
3875:
3796:
3704:
3702:{\displaystyle f_{c}}
3670:
3616:
3559:
3487:
3447:
3404:
3263:
3076:
2975:
2907:
2880:
2812:
2785:
2755:
2643:
2557:
2505:
2422:
2342:
2249:
2195:
2165:
2145:
2074:
1990:
1905:
1825:
1785:
1728:
1666:
1617:
1491:
1441:
1226:
1206:
1162:
1127:
998:
969:
870:
822:
732:
730:{\displaystyle V_{i}}
705:
661:
551:
449:ideal low-pass filter
430:
414:
381:subtractive synthesis
217:anti-aliasing filters
27:Type of signal filter
6065:
6001:
5868:
5841:
5751:
5718:
5696:
5645:
5592:
5570:
5525:
5492:
5469:
5436:
5409:
5389:
5235:
5213:
5174:
4928:
4841:
4830:or equivalently (in
4757:
4715:
4578:
4497:all-pole filter is 6
4395:is the filter order.
4358:
4297:improve this section
4170:
4102:
4082:
3978:, and time constant
3927:
3895:
3811:
3716:
3686:
3625:
3574:
3503:
3469:
3420:
3416:is within the range
3285:
3094:
2987:
2916:
2889:
2821:
2794:
2767:
2661:
2582:
2530:
2449:
2369:
2274:
2178:
2154:
2087:
1999:
1922:
1837:
1794:
1737:
1677:
1629:
1503:
1453:
1238:
1215:
1171:
1148:
1010:
996:{\displaystyle H(s)}
978:
887:
834:
744:
714:
678:
570:
461:rectangular function
389:anti-aliasing filter
368:transmission channel
54:improve this article
6520:Synthesiser modules
5305:
5128:oscillator circuits
5108:harmonic oscillator
5033:. It consists of a
4964:alternating current
4475:second-order filter
3412:By definition, the
3086:recurrence relation
2231:, are widely used.
1673:Using the notation
1142:difference equation
323:and other types of
6152:Electronics portal
6103:
6045:
5955:
5942:
5887:
5854:
5820:
5737:
5702:
5682:
5631:
5576:
5556:
5511:
5475:
5455:
5422:
5395:
5385:In this equation,
5373:
5291:
5219:
5199:
5080:electrical circuit
5072:
5031:electronic filters
4980:frequency response
4949:
4887:
4817:
4732:
4685:
4618:
4519:Butterworth filter
4479:Butterworth filter
4429:first-order filter
4397:
4377:
4224:
4156:
4088:
3954:
3909:
3870:
3791:
3699:
3665:
3611:
3554:
3482:
3442:
3399:
3258:
3175:Input contribution
3071:
2970:
2902:
2875:
2807:
2780:
2750:
2638:
2552:
2500:
2417:
2337:
2255:
2250:A simple low-pass
2229:Fourier transforms
2210:Bilinear transform
2190:
2160:
2140:
2069:
1985:
1900:
1820:
1780:
1723:
1661:
1612:
1486:
1436:
1221:
1201:
1160:{\displaystyle nT}
1157:
1122:
993:
964:
879:Frequency response
865:
817:
727:
700:
656:
557:
552:A simple low-pass
457:frequency response
445:
425:
419:, the time-domain
300:determined by its
158:frequency response
6510:Signal processing
6497:
6496:
6491:Electronic filter
6406:transfer function
6101:
6075:
6043:
6011:
5994:) is defined as:
5983:in the passband.
5963:Op amp integrator
5818:
5705:{\displaystyle Q}
5610:
5579:{\displaystyle K}
5478:{\displaystyle Q}
5398:{\displaystyle f}
5361:
5317:
5222:{\displaystyle f}
4885:
4867:
4815:
4791:
4695:in series with a
4616:
4589:
4588:
4585:
4558:Laplace transform
4501:dB per octave (20
4449:transfer function
4413:cutoff frequency,
4333:
4332:
4325:
4265:Fourier transform
4257:simplest case, a
3887:=0.5, then the
3865:
3789:
3660:
3609:
3545:
3394:
3352:
3254:
3252:
3247:
3237:
3178:
3176:
3171:
3161:
3066:
2899:
2804:
2745:
2730:
2693:
2671:
2636:
2621:
2524:
2523:
2498:
2441:
2440:
2405:
2361:
2360:
2306:
2284:
2163:{\displaystyle T}
2097:
2009:
1224:{\displaystyle T}
1120:
1085:
962:
863:
754:
688:
654:
639:
602:
580:
527:continuous signal
507:ringing artifacts
486:Real filters for
465:brick-wall filter
441:Angular frequency
343:low-pass filter.
237:signal processing
170:treble-cut filter
130:
129:
122:
104:
69:"Low-pass filter"
16:(Redirected from
6542:
6480:Band-stop filter
6475:Band-pass filter
6442:
6435:
6428:
6419:
6418:
6412:C code generator
6378:
6373:
6367:
6354:
6348:
6347:
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6325:
6319:
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6312:
6304:
6296:
6287:
6282:
6276:
6275:
6273:
6272:
6257:
6251:
6250:
6248:
6247:
6236:
6230:
6229:
6213:
6200:
6194:
6193:
6192:
6191:
6179:
6154:
6149:
6148:
6112:
6110:
6109:
6104:
6102:
6100:
6096:
6095:
6082:
6077:
6076:
6073:
6054:
6052:
6051:
6046:
6044:
6042:
6038:
6037:
6018:
6013:
6012:
6009:
5979:that allows for
5936:=3/2 henry and L
5918:cutoff frequency
5896:
5894:
5893:
5888:
5886:
5885:
5863:
5861:
5860:
5855:
5853:
5852:
5829:
5827:
5826:
5821:
5819:
5817:
5816:
5815:
5803:
5802:
5783:
5766:
5765:
5746:
5744:
5743:
5738:
5736:
5735:
5711:
5709:
5708:
5703:
5691:
5689:
5688:
5683:
5660:
5659:
5640:
5638:
5637:
5632:
5630:
5629:
5611:
5609:
5608:
5596:
5585:
5583:
5582:
5577:
5565:
5563:
5562:
5557:
5540:
5539:
5520:
5518:
5517:
5512:
5510:
5509:
5484:
5482:
5481:
5476:
5464:
5462:
5461:
5456:
5454:
5453:
5431:
5429:
5428:
5423:
5421:
5420:
5404:
5402:
5401:
5396:
5382:
5380:
5379:
5374:
5362:
5360:
5353:
5352:
5340:
5339:
5318:
5310:
5304:
5299:
5287:
5286:
5267:
5250:
5249:
5228:
5226:
5225:
5220:
5208:
5206:
5205:
5200:
5189:
5188:
5152:high-pass filter
5148:band-stop filter
5144:band-pass filter
5082:consisting of a
5002:electric circuit
4968:short circuiting
4958:
4956:
4955:
4950:
4948:
4947:
4946:
4896:
4894:
4893:
4888:
4886:
4884:
4873:
4868:
4860:
4855:
4854:
4853:
4826:
4824:
4823:
4818:
4816:
4814:
4797:
4792:
4790:
4776:
4771:
4770:
4769:
4748:cutoff frequency
4741:
4739:
4738:
4733:
4627:
4625:
4624:
4619:
4617:
4615:
4598:
4590:
4586:
4583:
4582:
4562:impulse response
4552:Laplace notation
4546:cutoff frequency
4523:Chebyshev filter
4515:cutoff frequency
4504:
4500:
4496:
4445:cutoff frequency
4434:
4405:cutoff frequency
4391:dB/decade where
4386:
4384:
4383:
4378:
4370:
4369:
4353:cutoff frequency
4328:
4321:
4317:
4314:
4308:
4277:
4269:
4233:
4231:
4230:
4225:
4220:
4219:
4199:
4198:
4185:
4184:
4165:
4163:
4162:
4157:
4152:
4151:
4131:
4130:
4117:
4116:
4097:
4095:
4094:
4089:
3963:
3961:
3960:
3955:
3939:
3938:
3918:
3916:
3915:
3910:
3886:
3879:
3877:
3876:
3871:
3866:
3864:
3863:
3862:
3828:
3823:
3822:
3800:
3798:
3797:
3792:
3790:
3788:
3781:
3780:
3771:
3770:
3754:
3753:
3752:
3743:
3742:
3726:
3709:are related by,
3708:
3706:
3705:
3700:
3698:
3697:
3681:
3674:
3672:
3671:
3666:
3661:
3659:
3658:
3657:
3638:
3620:
3618:
3617:
3612:
3610:
3608:
3591:
3586:
3585:
3563:
3561:
3560:
3555:
3550:
3546:
3541:
3530:
3524:
3523:
3495:
3491:
3489:
3488:
3483:
3481:
3480:
3464:
3455:
3451:
3449:
3448:
3443:
3414:smoothing factor
3408:
3406:
3405:
3400:
3395:
3393:
3392:
3391:
3372:
3371:
3362:
3353:
3350:
3347:
3346:
3313:
3312:
3297:
3296:
3267:
3265:
3264:
3259:
3253:
3250:
3248:
3243:
3242:
3238:
3236:
3235:
3234:
3215:
3207:
3201:
3200:
3184:
3182:
3177:
3174:
3172:
3167:
3166:
3162:
3160:
3159:
3158:
3139:
3138:
3129:
3123:
3122:
3112:
3110:
3106:
3105:
3080:
3078:
3077:
3072:
3067:
3065:
3064:
3055:
3054:
3053:
3035:
3034:
3024:
3012:
3011:
2999:
2998:
2979:
2977:
2976:
2971:
2966:
2965:
2945:
2944:
2931:
2930:
2911:
2909:
2908:
2903:
2901:
2900:
2897:
2884:
2882:
2881:
2876:
2871:
2870:
2850:
2849:
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2835:
2816:
2814:
2813:
2808:
2806:
2805:
2802:
2789:
2787:
2786:
2781:
2779:
2778:
2759:
2757:
2756:
2751:
2746:
2744:
2733:
2732:
2731:
2728:
2715:
2695:
2694:
2691:
2673:
2672:
2669:
2647:
2645:
2644:
2639:
2637:
2635:
2624:
2623:
2622:
2619:
2606:
2565:
2561:
2559:
2558:
2553:
2542:
2541:
2518:
2509:
2507:
2506:
2501:
2499:
2497:
2486:
2485:
2484:
2468:
2443:
2435:
2426:
2424:
2423:
2418:
2407:
2406:
2403:
2381:
2380:
2363:
2355:
2346:
2344:
2343:
2338:
2308:
2307:
2304:
2286:
2285:
2282:
2268:
2259:Kirchhoff's Laws
2199:
2197:
2196:
2191:
2169:
2167:
2166:
2161:
2149:
2147:
2146:
2141:
2121:
2120:
2099:
2098:
2095:
2078:
2076:
2075:
2070:
2065:
2064:
2060:
2059:
2033:
2032:
2011:
2010:
2007:
1994:
1992:
1991:
1986:
1984:
1983:
1956:
1955:
1934:
1933:
1909:
1907:
1906:
1901:
1899:
1898:
1871:
1870:
1849:
1848:
1829:
1827:
1826:
1821:
1819:
1818:
1806:
1805:
1789:
1787:
1786:
1781:
1767:
1766:
1765:
1749:
1748:
1732:
1730:
1729:
1724:
1710:
1709:
1708:
1689:
1688:
1670:
1668:
1667:
1662:
1660:
1659:
1655:
1654:
1621:
1619:
1618:
1613:
1611:
1610:
1559:
1558:
1557:
1523:
1522:
1521:
1495:
1493:
1492:
1487:
1473:
1472:
1471:
1445:
1443:
1442:
1437:
1432:
1431:
1406:
1405:
1379:
1378:
1363:
1362:
1355:
1354:
1328:
1327:
1291:
1290:
1289:
1258:
1257:
1256:
1230:
1228:
1227:
1222:
1210:
1208:
1207:
1202:
1166:
1164:
1163:
1158:
1131:
1129:
1128:
1123:
1121:
1119:
1118:
1117:
1101:
1100:
1091:
1086:
1084:
1074:
1073:
1072:
1058:
1048:
1047:
1046:
1029:
1002:
1000:
999:
994:
973:
971:
970:
965:
963:
961:
951:
950:
949:
935:
925:
924:
923:
906:
874:
872:
871:
866:
864:
862:
851:
846:
845:
826:
824:
823:
818:
810:
809:
805:
804:
778:
777:
756:
755:
752:
736:
734:
733:
728:
726:
725:
709:
707:
706:
701:
690:
689:
686:
665:
663:
662:
657:
655:
653:
642:
641:
640:
637:
624:
604:
603:
600:
582:
581:
578:
561:Kirchhoff's Laws
511:Gibbs phenomenon
473:impulse response
453:cutoff frequency
421:impulse response
333:electric guitars
302:RC time constant
298:cutoff frequency
244:prototype filter
174:high-pass filter
150:cutoff frequency
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
6550:
6549:
6545:
6544:
6543:
6541:
6540:
6539:
6500:
6499:
6498:
6493:
6484:
6470:All-pass filter
6451:
6446:
6387:
6382:
6381:
6374:
6370:
6355:
6351:
6335:
6334:
6326:
6322:
6306:
6305:
6297:
6290:
6283:
6279:
6270:
6268:
6259:
6258:
6254:
6245:
6243:
6242:. Epanorama.net
6238:
6237:
6233:
6226:
6201:
6197:
6189:
6187:
6181:
6180:
6173:
6168:
6150:
6143:
6140:
6129:
6122:
6091:
6087:
6086:
6081:
6072:
6068:
6066:
6063:
6062:
6033:
6029:
6022:
6017:
6008:
6004:
6002:
5999:
5998:
5965:
5947:
5939:
5935:
5931:
5927:
5923:
5903:
5875:
5871:
5869:
5866:
5865:
5848:
5844:
5842:
5839:
5838:
5834:
5811:
5807:
5792:
5788:
5787:
5782:
5758:
5754:
5752:
5749:
5748:
5731:
5727:
5719:
5716:
5715:
5697:
5694:
5693:
5652:
5648:
5646:
5643:
5642:
5619:
5615:
5604:
5600:
5595:
5593:
5590:
5589:
5571:
5568:
5567:
5532:
5528:
5526:
5523:
5522:
5505:
5501:
5493:
5490:
5489:
5470:
5467:
5466:
5443:
5439:
5437:
5434:
5433:
5416:
5412:
5410:
5407:
5406:
5390:
5387:
5386:
5348:
5344:
5329:
5325:
5309:
5300:
5295:
5276:
5272:
5271:
5266:
5242:
5238:
5236:
5233:
5232:
5214:
5211:
5210:
5181:
5177:
5175:
5172:
5171:
5168:
5140:television sets
5136:radio receivers
5064:
5059:
4994:
4988:
4936:
4935:
4931:
4929:
4926:
4925:
4877:
4872:
4859:
4849:
4848:
4844:
4842:
4839:
4838:
4801:
4796:
4780:
4775:
4765:
4764:
4760:
4758:
4755:
4754:
4716:
4713:
4712:
4677:
4671:
4666:
4661:
4602:
4597:
4581:
4579:
4576:
4575:
4554:
4505:dB per decade).
4502:
4498:
4494:
4432:
4365:
4361:
4359:
4356:
4355:
4345:
4329:
4318:
4312:
4309:
4294:
4278:
4267:
4259:running average
4250:
4215:
4211:
4194:
4190:
4180:
4176:
4171:
4168:
4167:
4147:
4143:
4126:
4122:
4112:
4108:
4103:
4100:
4099:
4083:
4080:
4079:
4057:
4038:outputs can be
4028:
3934:
3930:
3928:
3925:
3924:
3896:
3893:
3892:
3884:
3858:
3854:
3832:
3827:
3818:
3814:
3812:
3809:
3808:
3776:
3772:
3766:
3762:
3755:
3748:
3744:
3738:
3734:
3727:
3725:
3717:
3714:
3713:
3693:
3689:
3687:
3684:
3683:
3679:
3653:
3649:
3642:
3637:
3626:
3623:
3622:
3595:
3590:
3581:
3577:
3575:
3572:
3571:
3567:Recalling that
3531:
3529:
3525:
3519:
3515:
3504:
3501:
3500:
3493:
3476:
3472:
3470:
3467:
3466:
3460:
3453:
3421:
3418:
3417:
3387:
3383:
3373:
3367:
3363:
3361:
3349:
3336:
3332:
3308:
3304:
3292:
3288:
3286:
3283:
3282:
3249:
3230:
3226:
3216:
3208:
3206:
3202:
3190:
3186:
3185:
3183:
3173:
3154:
3150:
3140:
3134:
3130:
3128:
3124:
3118:
3114:
3113:
3111:
3101:
3097:
3095:
3092:
3091:
3060:
3056:
3043:
3039:
3030:
3026:
3025:
3023:
3007:
3003:
2994:
2990:
2988:
2985:
2984:
2961:
2957:
2940:
2936:
2926:
2922:
2917:
2914:
2913:
2896:
2892:
2890:
2887:
2886:
2866:
2862:
2845:
2841:
2831:
2827:
2822:
2819:
2818:
2801:
2797:
2795:
2792:
2791:
2774:
2770:
2768:
2765:
2764:
2734:
2727:
2723:
2716:
2714:
2690:
2686:
2668:
2664:
2662:
2659:
2658:
2625:
2618:
2614:
2607:
2605:
2583:
2580:
2579:
2563:
2537:
2533:
2531:
2528:
2527:
2487:
2480:
2476:
2469:
2467:
2450:
2447:
2446:
2402:
2398:
2376:
2372:
2370:
2367:
2366:
2303:
2299:
2281:
2277:
2275:
2272:
2271:
2237:
2217:digital filters
2213:
2206:
2179:
2176:
2175:
2155:
2152:
2151:
2116:
2112:
2094:
2090:
2088:
2085:
2084:
2055:
2051:
2047:
2043:
2028:
2024:
2006:
2002:
2000:
1997:
1996:
1979:
1975:
1945:
1941:
1929:
1925:
1923:
1920:
1919:
1916:
1894:
1890:
1860:
1856:
1844:
1840:
1838:
1835:
1834:
1814:
1810:
1801:
1797:
1795:
1792:
1791:
1758:
1757:
1753:
1744:
1740:
1738:
1735:
1734:
1698:
1697:
1693:
1684:
1680:
1678:
1675:
1674:
1650:
1646:
1642:
1638:
1630:
1627:
1626:
1606:
1602:
1547:
1546:
1542:
1511:
1510:
1506:
1504:
1501:
1500:
1461:
1460:
1456:
1454:
1451:
1450:
1401:
1397:
1393:
1389:
1374:
1370:
1350:
1346:
1342:
1338:
1323:
1319:
1279:
1278:
1274:
1246:
1245:
1241:
1239:
1236:
1235:
1216:
1213:
1212:
1172:
1169:
1168:
1149:
1146:
1145:
1138:
1113:
1109:
1102:
1096:
1092:
1090:
1065:
1064:
1060:
1059:
1036:
1035:
1031:
1030:
1028:
1011:
1008:
1007:
979:
976:
975:
942:
941:
937:
936:
913:
912:
908:
907:
905:
888:
885:
884:
881:
855:
850:
841:
837:
835:
832:
831:
800:
796:
792:
788:
773:
769:
751:
747:
745:
742:
741:
721:
717:
715:
712:
711:
685:
681:
679:
676:
675:
672:
643:
636:
632:
625:
623:
599:
595:
577:
573:
571:
568:
567:
543:
529:from a sampled
409:
310:current divider
260:
225:digital filters
166:high-cut filter
134:low-pass filter
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
6548:
6538:
6537:
6532:
6527:
6522:
6517:
6515:Linear filters
6512:
6495:
6494:
6489:
6486:
6485:
6483:
6482:
6477:
6472:
6467:
6462:
6456:
6453:
6452:
6445:
6444:
6437:
6430:
6422:
6416:
6415:
6409:
6399:
6393:
6386:
6385:External links
6383:
6380:
6379:
6368:
6349:
6320:
6288:
6277:
6252:
6231:
6224:
6195:
6170:
6169:
6167:
6164:
6163:
6162:
6156:
6155:
6139:
6136:
6127:
6120:
6114:
6113:
6099:
6094:
6090:
6085:
6080:
6071:
6056:
6055:
6041:
6036:
6032:
6028:
6025:
6021:
6016:
6007:
5946:
5943:
5937:
5933:
5929:
5925:
5921:
5914:Cauer topology
5902:
5899:
5884:
5881:
5878:
5874:
5851:
5847:
5832:
5831:
5814:
5810:
5806:
5801:
5798:
5795:
5791:
5786:
5781:
5778:
5775:
5772:
5769:
5764:
5761:
5757:
5734:
5730:
5726:
5723:
5713:
5701:
5681:
5678:
5675:
5672:
5669:
5666:
5663:
5658:
5655:
5651:
5628:
5625:
5622:
5618:
5614:
5607:
5603:
5599:
5587:
5575:
5555:
5552:
5549:
5546:
5543:
5538:
5535:
5531:
5508:
5504:
5500:
5497:
5474:
5452:
5449:
5446:
5442:
5419:
5415:
5394:
5372:
5369:
5366:
5359:
5356:
5351:
5347:
5343:
5338:
5335:
5332:
5328:
5324:
5321:
5316:
5313:
5308:
5303:
5298:
5294:
5290:
5285:
5282:
5279:
5275:
5270:
5265:
5262:
5259:
5256:
5253:
5248:
5245:
5241:
5218:
5198:
5195:
5192:
5187:
5184:
5180:
5167:
5164:
5063:
5060:
5058:
5055:
5047:voltage source
5018:current source
4990:Main article:
4987:
4984:
4972:
4971:
4960:
4945:
4942:
4939:
4934:
4922:direct current
4910:
4909:
4905:
4898:
4897:
4883:
4880:
4876:
4871:
4866:
4863:
4858:
4852:
4847:
4828:
4827:
4813:
4810:
4807:
4804:
4800:
4795:
4789:
4786:
4783:
4779:
4774:
4768:
4763:
4731:
4728:
4724:
4720:
4711:of the filter
4691:consists of a
4673:Main article:
4670:
4667:
4665:
4662:
4660:
4657:
4639:is the filter
4629:
4628:
4614:
4611:
4608:
4605:
4601:
4596:
4593:
4553:
4550:
4507:
4506:
4491:
4471:
4463:Pole–zero plot
4376:
4373:
4368:
4364:
4344:
4341:
4331:
4330:
4281:
4279:
4272:
4266:
4263:
4249:
4246:
4223:
4218:
4214:
4209:
4206:
4202:
4197:
4193:
4188:
4183:
4179:
4175:
4155:
4150:
4146:
4141:
4138:
4134:
4129:
4125:
4120:
4115:
4111:
4107:
4087:
4044:
3973:
3953:
3950:
3947:
3943:
3937:
3933:
3908:
3904:
3900:
3881:
3880:
3869:
3861:
3857:
3853:
3850:
3847:
3844:
3841:
3838:
3835:
3831:
3826:
3821:
3817:
3802:
3801:
3787:
3784:
3779:
3775:
3769:
3765:
3761:
3758:
3751:
3747:
3741:
3737:
3733:
3730:
3724:
3721:
3696:
3692:
3676:
3675:
3664:
3656:
3652:
3648:
3645:
3641:
3636:
3633:
3630:
3607:
3604:
3601:
3598:
3594:
3589:
3584:
3580:
3565:
3564:
3553:
3549:
3544:
3540:
3537:
3534:
3528:
3522:
3518:
3514:
3511:
3508:
3479:
3475:
3441:
3437:
3433:
3429:
3425:
3410:
3409:
3398:
3390:
3386:
3382:
3379:
3376:
3370:
3366:
3360:
3357:
3345:
3342:
3339:
3335:
3331:
3328:
3325:
3322:
3319:
3316:
3311:
3307:
3303:
3300:
3295:
3291:
3269:
3268:
3257:
3246:
3241:
3233:
3229:
3225:
3222:
3219:
3214:
3211:
3205:
3199:
3196:
3193:
3189:
3181:
3170:
3165:
3157:
3153:
3149:
3146:
3143:
3137:
3133:
3127:
3121:
3117:
3109:
3104:
3100:
3082:
3081:
3070:
3063:
3059:
3052:
3049:
3046:
3042:
3038:
3033:
3029:
3021:
3018:
3015:
3010:
3006:
3002:
2997:
2993:
2969:
2964:
2960:
2955:
2952:
2948:
2943:
2939:
2934:
2929:
2925:
2921:
2895:
2874:
2869:
2865:
2860:
2857:
2853:
2848:
2844:
2839:
2834:
2830:
2826:
2800:
2777:
2773:
2761:
2760:
2749:
2743:
2740:
2737:
2726:
2722:
2719:
2713:
2710:
2707:
2704:
2701:
2698:
2689:
2685:
2682:
2679:
2676:
2667:
2634:
2631:
2628:
2617:
2613:
2610:
2604:
2600:
2596:
2593:
2590:
2587:
2572:into equation
2551:
2548:
2545:
2540:
2536:
2522:
2521:
2512:
2510:
2496:
2493:
2490:
2483:
2479:
2475:
2472:
2466:
2463:
2460:
2457:
2454:
2439:
2438:
2429:
2427:
2416:
2413:
2410:
2401:
2396:
2393:
2390:
2387:
2384:
2379:
2375:
2359:
2358:
2349:
2347:
2336:
2333:
2330:
2327:
2323:
2320:
2317:
2314:
2311:
2302:
2298:
2295:
2292:
2289:
2280:
2236:
2233:
2205:
2202:
2189:
2186:
2183:
2159:
2139:
2136:
2133:
2130:
2127:
2124:
2119:
2115:
2111:
2108:
2105:
2102:
2093:
2068:
2063:
2058:
2054:
2050:
2046:
2042:
2039:
2036:
2031:
2027:
2023:
2020:
2017:
2014:
2005:
1982:
1978:
1974:
1971:
1968:
1965:
1962:
1959:
1954:
1951:
1948:
1944:
1940:
1937:
1932:
1928:
1915:
1914:Error analysis
1912:
1911:
1910:
1897:
1893:
1889:
1886:
1883:
1880:
1877:
1874:
1869:
1866:
1863:
1859:
1855:
1852:
1847:
1843:
1817:
1813:
1809:
1804:
1800:
1779:
1776:
1773:
1770:
1764:
1761:
1756:
1752:
1747:
1743:
1722:
1719:
1716:
1713:
1707:
1704:
1701:
1696:
1692:
1687:
1683:
1658:
1653:
1649:
1645:
1641:
1637:
1634:
1623:
1622:
1609:
1605:
1601:
1598:
1595:
1592:
1589:
1586:
1583:
1580:
1577:
1574:
1571:
1568:
1565:
1562:
1556:
1553:
1550:
1545:
1541:
1538:
1535:
1532:
1529:
1526:
1520:
1517:
1514:
1509:
1485:
1482:
1479:
1476:
1470:
1467:
1464:
1459:
1447:
1446:
1435:
1430:
1427:
1424:
1421:
1418:
1415:
1412:
1409:
1404:
1400:
1396:
1392:
1388:
1385:
1382:
1377:
1373:
1369:
1366:
1361:
1358:
1353:
1349:
1345:
1341:
1337:
1334:
1331:
1326:
1322:
1318:
1315:
1312:
1309:
1306:
1303:
1300:
1297:
1294:
1288:
1285:
1282:
1277:
1273:
1270:
1267:
1264:
1261:
1255:
1252:
1249:
1244:
1220:
1200:
1197:
1194:
1191:
1188:
1185:
1182:
1179:
1176:
1156:
1153:
1137:
1134:
1133:
1132:
1116:
1112:
1108:
1105:
1099:
1095:
1089:
1083:
1080:
1077:
1071:
1068:
1063:
1057:
1054:
1051:
1045:
1042:
1039:
1034:
1027:
1024:
1021:
1018:
1015:
992:
989:
986:
983:
960:
957:
954:
948:
945:
940:
934:
931:
928:
922:
919:
916:
911:
904:
901:
898:
895:
892:
880:
877:
861:
858:
854:
849:
844:
840:
828:
827:
816:
813:
808:
803:
799:
795:
791:
787:
784:
781:
776:
772:
768:
765:
762:
759:
750:
724:
720:
699:
696:
693:
684:
671:
668:
667:
666:
652:
649:
646:
635:
631:
628:
622:
619:
616:
613:
610:
607:
598:
594:
591:
588:
585:
576:
542:
539:
531:digital signal
408:
405:
397:reconstruction
283:optical filter
259:
256:
233:moving average
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
6547:
6536:
6533:
6531:
6528:
6526:
6523:
6521:
6518:
6516:
6513:
6511:
6508:
6507:
6505:
6492:
6487:
6481:
6478:
6476:
6473:
6471:
6468:
6466:
6463:
6461:
6458:
6457:
6454:
6450:
6443:
6438:
6436:
6431:
6429:
6424:
6423:
6420:
6413:
6410:
6407:
6403:
6400:
6397:
6394:
6392:
6389:
6388:
6377:
6372:
6366:
6365:9780750300582
6362:
6359:
6353:
6345:
6339:
6331:
6324:
6316:
6310:
6302:
6295:
6293:
6286:
6281:
6267:on 2013-09-27
6266:
6262:
6256:
6241:
6235:
6227:
6225:0-03-051648-X
6221:
6217:
6212:
6211:
6205:
6199:
6186:
6185:
6178:
6176:
6171:
6161:
6158:
6157:
6153:
6147:
6142:
6135:
6133:
6126:
6119:
6097:
6092:
6088:
6083:
6078:
6069:
6061:
6060:
6059:
6039:
6034:
6030:
6026:
6023:
6019:
6014:
6005:
5997:
5996:
5995:
5993:
5989:
5984:
5982:
5978:
5977:active filter
5975:to create an
5974:
5973:active device
5970:
5964:
5960:
5951:
5928:=4/3 farad, R
5919:
5915:
5910:
5906:
5898:
5882:
5879:
5876:
5872:
5849:
5845:
5835:
5812:
5808:
5804:
5799:
5796:
5793:
5789:
5784:
5779:
5776:
5770:
5762:
5759:
5755:
5732:
5728:
5724:
5721:
5714:
5699:
5679:
5676:
5673:
5670:
5664:
5656:
5653:
5649:
5626:
5623:
5620:
5616:
5612:
5605:
5601:
5597:
5588:
5573:
5553:
5550:
5544:
5536:
5533:
5529:
5506:
5502:
5498:
5495:
5488:
5487:
5486:
5472:
5450:
5447:
5444:
5440:
5417:
5413:
5392:
5383:
5367:
5357:
5354:
5349:
5345:
5341:
5336:
5333:
5330:
5326:
5322:
5319:
5314:
5311:
5306:
5301:
5296:
5292:
5288:
5283:
5280:
5277:
5273:
5268:
5263:
5260:
5254:
5246:
5243:
5239:
5230:
5216:
5193:
5185:
5182:
5178:
5163:
5161:
5157:
5153:
5149:
5145:
5141:
5137:
5134:, such as in
5133:
5129:
5124:
5122:
5117:
5113:
5109:
5105:
5101:
5097:
5093:
5089:
5085:
5081:
5077:
5068:
5054:
5052:
5048:
5044:
5040:
5036:
5032:
5029:
5026:
5021:
5019:
5015:
5011:
5007:
5003:
4999:
4993:
4983:
4981:
4977:
4969:
4965:
4961:
4932:
4923:
4919:
4918:
4917:
4915:
4906:
4903:
4902:
4901:
4881:
4878:
4874:
4869:
4864:
4861:
4856:
4845:
4837:
4836:
4835:
4834:per second):
4833:
4811:
4808:
4805:
4802:
4798:
4793:
4787:
4784:
4781:
4777:
4772:
4761:
4753:
4752:
4751:
4749:
4745:
4729:
4726:
4722:
4718:
4710:
4709:time constant
4706:
4702:
4698:
4694:
4690:
4681:
4676:
4656:
4654:
4650:
4646:
4642:
4641:time constant
4638:
4634:
4612:
4609:
4606:
4603:
4599:
4594:
4591:
4574:
4573:
4572:
4569:
4567:
4563:
4559:
4549:
4547:
4542:
4540:
4536:
4532:
4528:
4527:Bessel filter
4524:
4520:
4516:
4512:
4492:
4489:
4485:
4480:
4476:
4472:
4470:
4468:
4464:
4458:
4455:as well as a
4454:
4450:
4446:
4442:
4438:
4430:
4426:
4425:
4424:
4422:
4418:
4414:
4410:
4406:
4402:
4394:
4390:
4374:
4371:
4366:
4362:
4354:
4349:
4340:
4337:
4327:
4324:
4316:
4306:
4302:
4298:
4292:
4291:
4287:
4282:This section
4280:
4276:
4271:
4270:
4262:
4260:
4255:
4254:sinc function
4245:
4243:
4239:
4238:
4216:
4212:
4207:
4204:
4200:
4195:
4191:
4186:
4181:
4177:
4148:
4144:
4139:
4136:
4132:
4127:
4123:
4118:
4113:
4109:
4085:
4077:
4074:
4073:time constant
4070:
4066:
4062:
4055:
4051:
4047:
4043:
4041:
4037:
4033:
4026:
4022:
4018:
4014:
4010:
4007:
4003:
4000:
3996:
3992:
3988:
3984:
3981:
3977:
3972:
3970:
3965:
3951:
3948:
3945:
3941:
3935:
3922:
3906:
3902:
3898:
3890:
3867:
3859:
3851:
3848:
3842:
3839:
3836:
3829:
3824:
3819:
3815:
3807:
3806:
3805:
3785:
3782:
3777:
3773:
3767:
3759:
3756:
3749:
3745:
3739:
3731:
3728:
3722:
3719:
3712:
3711:
3710:
3694:
3690:
3662:
3654:
3650:
3646:
3643:
3639:
3634:
3631:
3628:
3605:
3602:
3599:
3596:
3592:
3587:
3582:
3578:
3570:
3569:
3568:
3551:
3547:
3542:
3538:
3535:
3532:
3526:
3520:
3512:
3509:
3506:
3499:
3498:
3497:
3477:
3463:
3459:
3458:time constant
3439:
3435:
3431:
3427:
3423:
3415:
3396:
3388:
3380:
3377:
3374:
3368:
3358:
3355:
3343:
3340:
3337:
3333:
3326:
3323:
3320:
3314:
3309:
3305:
3301:
3298:
3293:
3289:
3281:
3280:
3279:
3278:
3274:
3255:
3244:
3239:
3231:
3223:
3220:
3217:
3212:
3209:
3203:
3197:
3194:
3191:
3187:
3179:
3168:
3163:
3155:
3147:
3144:
3141:
3135:
3125:
3119:
3115:
3107:
3102:
3098:
3090:
3089:
3088:
3087:
3068:
3061:
3050:
3047:
3044:
3040:
3036:
3031:
3027:
3019:
3016:
3013:
3008:
3004:
3000:
2995:
2991:
2983:
2982:
2981:
2962:
2958:
2953:
2950:
2946:
2941:
2937:
2932:
2927:
2923:
2893:
2867:
2863:
2858:
2855:
2851:
2846:
2842:
2837:
2832:
2828:
2798:
2775:
2747:
2741:
2738:
2724:
2720:
2711:
2708:
2705:
2699:
2687:
2683:
2677:
2665:
2657:
2656:
2655:
2653:
2652:
2632:
2629:
2615:
2611:
2602:
2598:
2591:
2585:
2577:
2576:
2571:
2570:
2546:
2538:
2534:
2520:
2513:
2511:
2494:
2491:
2481:
2477:
2473:
2464:
2458:
2452:
2445:
2444:
2437:
2430:
2428:
2411:
2399:
2394:
2391:
2385:
2377:
2373:
2365:
2364:
2357:
2350:
2348:
2331:
2325:
2321:
2318:
2312:
2300:
2296:
2290:
2278:
2270:
2269:
2266:
2264:
2260:
2253:
2248:
2244:
2242:
2232:
2230:
2226:
2222:
2218:
2211:
2201:
2187:
2181:
2173:
2157:
2134:
2131:
2125:
2122:
2117:
2113:
2109:
2103:
2091:
2082:
2061:
2056:
2052:
2048:
2044:
2040:
2037:
2029:
2025:
2021:
2015:
2003:
1980:
1976:
1969:
1966:
1963:
1957:
1952:
1949:
1946:
1942:
1938:
1935:
1930:
1926:
1895:
1891:
1884:
1881:
1878:
1872:
1867:
1864:
1861:
1857:
1853:
1850:
1845:
1841:
1833:
1832:
1831:
1815:
1811:
1807:
1802:
1798:
1774:
1771:
1754:
1750:
1745:
1741:
1717:
1714:
1694:
1690:
1685:
1681:
1671:
1656:
1651:
1647:
1643:
1639:
1635:
1632:
1607:
1603:
1596:
1593:
1590:
1584:
1578:
1572:
1569:
1566:
1543:
1539:
1536:
1530:
1527:
1507:
1499:
1498:
1497:
1480:
1477:
1457:
1425:
1419:
1416:
1413:
1402:
1398:
1394:
1390:
1386:
1383:
1375:
1371:
1367:
1359:
1356:
1351:
1347:
1343:
1339:
1335:
1332:
1324:
1320:
1316:
1310:
1304:
1301:
1298:
1275:
1271:
1265:
1262:
1242:
1234:
1233:
1232:
1218:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1154:
1151:
1143:
1114:
1110:
1106:
1103:
1097:
1093:
1087:
1078:
1061:
1052:
1032:
1025:
1019:
1013:
1006:
1005:
1004:
987:
981:
955:
938:
929:
909:
902:
896:
890:
876:
859:
856:
852:
847:
842:
838:
814:
806:
801:
797:
793:
789:
785:
782:
774:
770:
766:
760:
748:
740:
739:
738:
722:
718:
694:
682:
650:
647:
633:
629:
620:
617:
614:
608:
596:
592:
586:
574:
566:
565:
564:
562:
555:
550:
546:
541:Time response
538:
536:
532:
528:
524:
519:
516:
512:
508:
503:
501:
497:
493:
489:
484:
480:
478:
477:sinc function
474:
470:
466:
462:
458:
454:
450:
442:
438:
434:
429:
422:
418:
417:sinc function
413:
404:
402:
398:
394:
390:
385:
384:
382:
376:
371:
369:
365:
361:
358:signals (and
357:
353:
349:
348:DSL splitters
344:
342:
341:time constant
338:
334:
330:
326:
322:
317:
315:
311:
307:
303:
299:
295:
290:
288:
284:
279:
275:
273:
269:
265:
255:
253:
249:
245:
240:
238:
234:
230:
226:
222:
218:
214:
210:
205:
204:frequencies.
203:
199:
195:
191:
186:
182:
177:
175:
171:
167:
163:
162:filter design
159:
155:
151:
147:
143:
139:
135:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
6459:
6371:
6357:
6352:
6329:
6323:
6300:
6280:
6269:. Retrieved
6265:the original
6255:
6244:. Retrieved
6234:
6209:
6198:
6188:, retrieved
6183:
6124:
6117:
6115:
6057:
5985:
5968:
5966:
5904:
5836:
5833:
5384:
5231:
5169:
5156:second-order
5155:
5125:
5073:
5057:Second order
5045:driven by a
5041:, either in
5022:
5012:driven by a
5004:composed of
4995:
4973:
4911:
4899:
4829:
4686:
4644:
4636:
4632:
4630:
4570:
4555:
4543:
4538:
4530:
4514:
4508:
4474:
4460:
4428:
4420:
4412:
4398:
4392:
4388:
4338:
4334:
4319:
4310:
4295:Please help
4283:
4251:
4235:
4075:
4061:proportional
4058:
4053:
4049:
4045:
4035:
4029:
4024:
4020:
4016:
4012:
4008:
4005:
4001:
3998:
3994:
3990:
3986:
3982:
3979:
3975:
3966:
3920:
3888:
3882:
3803:
3677:
3566:
3461:
3413:
3411:
3272:
3270:
3083:
2762:
2649:
2573:
2567:
2525:
2514:
2431:
2351:
2256:
2241:discretizing
2238:
2214:
2172:time variant
2171:
2081:time variant
2080:
1917:
1672:
1624:
1449:Solving for
1448:
1139:
882:
829:
673:
558:
544:
520:
504:
485:
481:
446:
432:
386:
378:
375:synthesisers
372:
367:
345:
325:loudspeakers
318:
291:
286:
280:
276:
261:
241:
208:
206:
201:
197:
193:
189:
184:
180:
178:
169:
165:
140:that passes
133:
131:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
6204:Sedra, Adel
5940:=1/2 henry.
5104:capacitance
5076:RLC circuit
4664:First order
4566:Z-transform
4531:knee curves
4488:RLC circuit
4415:the filter
4069:exponential
2263:capacitance
2243:the model.
1140:A discrete
500:phase shift
469:convolution
339:is another
272:electronics
209:hiss filter
188:filters as
179:In optics,
6504:Categories
6271:2013-09-24
6246:2013-09-24
6190:2017-10-04
6166:References
6130:, and the
5957:See also:
5116:LC circuit
5100:inductance
5096:resistance
5062:RLC filter
4511:asymptotes
4467:RC circuit
4417:attenuates
4313:March 2015
4040:refactored
3969:pseudocode
2885:, and let
2083:, such as
674:If we let
433:Power gain
366:of wires (
337:integrator
321:subwoofers
190:short-pass
154:attenuates
80:newspapers
6530:Acoustics
6338:cite book
6309:cite book
6070:ω
6027:π
5932:=1 ohm, L
5805:⋅
5780:−
5777:≈
5725:≫
5551:≈
5499:≪
5342:⋅
5320:⋅
5289:⋅
5264:−
5092:capacitor
5010:inductors
5006:resistors
4998:RL filter
4986:RL filter
4976:Bode plot
4914:reactance
4865:τ
4846:ω
4806:π
4788:τ
4785:π
4719:τ
4705:reactance
4701:capacitor
4669:RC filter
4604:τ
4560:of their
4535:resonance
4401:Bode plot
4363:ω
4284:does not
4205:…
4137:…
4086:α
3946:α
3942:≈
3932:Δ
3903:≪
3899:α
3856:Δ
3852:π
3843:α
3840:−
3830:α
3764:Δ
3760:π
3736:Δ
3732:π
3720:α
3647:π
3600:π
3543:α
3539:α
3536:−
3517:Δ
3474:Δ
3436:≤
3432:α
3428:≤
3385:Δ
3365:Δ
3356:α
3341:−
3327:α
3324:−
3302:α
3245:⏞
3228:Δ
3195:−
3169:⏞
3152:Δ
3132:Δ
3058:Δ
3048:−
3037:−
3001:−
2951:…
2856:…
2772:Δ
2739:
2721:
2684:−
2630:
2612:
2492:
2474:
2297:−
2252:RC filter
2185:→
2132:ω
2126:
2053:ω
2049:−
2041:−
1970:β
1967:−
1950:−
1939:β
1885:β
1882:−
1865:−
1854:β
1648:ω
1644:−
1633:β
1597:β
1594:−
1570:−
1540:β
1417:−
1399:ω
1395:−
1387:−
1368:−
1348:ω
1344:−
1336:−
1302:−
1272:−
1111:ω
1094:ω
839:ω
798:ω
794:−
786:−
648:
630:
615:−
554:RC filter
492:windowing
488:real-time
471:with its
463:and is a
360:high-pass
294:RC filter
264:acoustics
252:band-stop
248:band-pass
198:high-pass
194:long-pass
181:high-pass
146:frequency
6160:Baseband
6138:See also
6132:stopband
5112:resonate
5090:, and a
5088:inductor
5084:resistor
5051:parallel
5039:inductor
5035:resistor
5025:analogue
4699:, and a
4693:resistor
4653:passband
4484:Q factor
3997:RC)
3985:lowpass(
3983:function
2654:so that
533:. Real
509:via the
395:and for
393:sampling
329:harmonic
306:parallel
287:longpass
258:Examples
229:blurring
211:used in
202:low-pass
185:low-pass
110:May 2023
5986:In the
5121:damping
5037:and an
5014:voltage
4908:amount.
4832:radians
4689:circuit
4647:is the
4409:rolloff
4305:removed
4290:sources
4237:inertia
3919:, then
1496:we get
1003:we get
391:before
144:with a
142:signals
94:scholar
18:Lowpass
6363:
6222:
5969:active
5961:, and
5132:tuning
5102:, and
5049:or in
5043:series
5000:is an
4962:Since
4920:Since
4643:, and
4631:where
4584:Output
4441:decade
4437:octave
4025:return
4004:y
3678:note
2578:gives
2526:where
1625:Where
1167:where
830:where
559:Using
268:optics
138:filter
96:
89:
82:
75:
67:
6535:Sound
5992:hertz
5086:, an
4587:Input
4539:above
4433:6 dB)
4421:order
3883:If
3351:where
2215:Many
459:is a
354:from
314:below
213:audio
168:, or
136:is a
101:JSTOR
87:books
6361:ISBN
6344:link
6315:link
6220:ISBN
5981:gain
5008:and
4978:and
4697:load
4649:gain
4465:and
4461:See
4457:pole
4453:zero
4288:any
4286:cite
4050:from
4032:loop
4030:The
4017:from
4009:real
4002:real
3995:real
3993:dt,
3991:real
3987:real
3804:and
3682:and
2223:and
1733:and
1211:and
521:The
475:, a
415:The
379:See
364:pair
356:POTS
270:and
200:and
192:and
183:and
152:and
73:news
5967:An
5138:or
5074:An
5016:or
4744:tau
4299:by
4046:for
4013:for
4006:var
3999:var
3989:x,
3907:0.5
3621:so
2898:out
2729:out
2692:out
2620:out
2404:out
2305:out
2123:sin
2008:out
753:out
638:out
579:out
447:An
399:in
370:).
352:DSL
316:.)
281:An
254:).
250:or
56:by
6506::
6340:}}
6336:{{
6311:}}
6307:{{
6291:^
6218:.
6216:60
6174:^
5747::
5641::
5521::
5146:,
5098:,
4655:.
4525:,
4521:,
4473:A
4427:A
4076:RC
4054:to
4052:2
4048:i
4027:y
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4019:2
4015:i
3980:RC
3976:dt
3964:.
3921:RC
3889:RC
3496:,
3462:RC
3359::=
3273:RC
2803:in
2670:in
2283:in
2265::
2200:.
2096:in
687:in
601:in
437:dB
403:.
377:.
274:.
266:,
223:,
215:,
176:.
132:A
6441:e
6434:t
6427:v
6346:)
6317:)
6274:.
6249:.
6228:.
6128:1
6125:R
6123:/
6121:2
6118:R
6098:C
6093:2
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6084:1
6079:=
6074:c
6040:C
6035:2
6031:R
6024:2
6020:1
6015:=
6010:c
6006:f
5938:3
5934:1
5930:4
5926:2
5922:c
5920:ω
5883:F
5880:S
5877:F
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5850:c
5846:f
5813:2
5809:f
5800:F
5797:S
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5790:f
5785:K
5774:)
5771:f
5768:(
5763:P
5760:L
5756:H
5733:c
5729:f
5722:f
5712:.
5700:Q
5680:Q
5677:K
5674:j
5671:=
5668:)
5665:f
5662:(
5657:P
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5650:H
5627:F
5624:S
5621:F
5617:f
5613:=
5606:c
5602:f
5598:f
5586:.
5574:K
5554:K
5548:)
5545:f
5542:(
5537:P
5534:L
5530:H
5507:c
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5496:f
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5418:c
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5368:1
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5261:=
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5252:(
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5217:f
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5191:(
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4944:t
4941:u
4938:o
4933:V
4882:C
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4870:=
4862:1
4857:=
4851:c
4812:C
4809:R
4803:2
4799:1
4794:=
4782:2
4778:1
4773:=
4767:c
4762:f
4730:C
4727:R
4723:=
4645:K
4637:τ
4633:s
4613:1
4610:+
4607:s
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4503:n
4499:n
4495:n
4490:.
4469:.
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4375:1
4372:=
4367:0
4326:)
4320:(
4315:)
4311:(
4307:.
4293:.
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4217:n
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3723:=
3695:c
3691:f
3680:α
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3644:2
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3632:C
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3606:C
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3583:c
3579:f
3552:.
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3507:R
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3397:.
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3299:=
3294:i
3290:y
3256:.
3240:)
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3108:=
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3069:.
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3009:i
3005:y
2996:i
2992:x
2968:)
2963:n
2959:y
2954:,
2947:,
2942:2
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2928:1
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2894:v
2873:)
2868:n
2864:x
2859:,
2852:,
2847:2
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2838:,
2833:1
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2825:(
2799:v
2776:T
2748:.
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2725:v
2718:d
2712:C
2709:R
2706:=
2703:)
2700:t
2697:(
2688:v
2681:)
2678:t
2675:(
2666:v
2651:V
2633:t
2627:d
2616:v
2609:d
2603:C
2599:=
2595:)
2592:t
2589:(
2586:i
2575:I
2569:Q
2564:t
2550:)
2547:t
2544:(
2539:c
2535:Q
2519:)
2517:I
2515:(
2495:t
2489:d
2482:c
2478:Q
2471:d
2465:=
2462:)
2459:t
2456:(
2453:i
2436:)
2434:Q
2432:(
2415:)
2412:t
2409:(
2400:v
2395:C
2392:=
2389:)
2386:t
2383:(
2378:c
2374:Q
2356:)
2354:V
2352:(
2335:)
2332:t
2329:(
2326:i
2322:R
2319:=
2316:)
2313:t
2310:(
2301:v
2294:)
2291:t
2288:(
2279:v
2212:.
2188:0
2182:T
2158:T
2138:)
2135:t
2129:(
2118:i
2114:V
2110:=
2107:)
2104:t
2101:(
2092:v
2067:)
2062:t
2057:0
2045:e
2038:1
2035:(
2030:i
2026:V
2022:=
2019:)
2016:t
2013:(
2004:v
1981:n
1977:v
1973:)
1964:1
1961:(
1958:+
1953:1
1947:n
1943:V
1936:=
1931:n
1927:V
1896:n
1892:v
1888:)
1879:1
1876:(
1873:+
1868:1
1862:n
1858:V
1851:=
1846:n
1842:V
1816:i
1812:V
1808:=
1803:n
1799:v
1778:)
1775:T
1772:n
1769:(
1763:n
1760:i
1755:v
1751:=
1746:n
1742:v
1721:)
1718:T
1715:n
1712:(
1706:t
1703:u
1700:o
1695:v
1691:=
1686:n
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1652:0
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1636:=
1608:i
1604:V
1600:)
1591:1
1588:(
1585:+
1582:)
1579:T
1576:)
1573:1
1567:n
1564:(
1561:(
1555:t
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1537:=
1534:)
1531:T
1528:n
1525:(
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1478:n
1475:(
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1429:)
1426:T
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1420:1
1414:n
1411:(
1408:(
1403:0
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1384:1
1381:(
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1372:V
1365:)
1360:T
1357:n
1352:0
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1333:1
1330:(
1325:i
1321:V
1317:=
1314:)
1311:T
1308:)
1305:1
1299:n
1296:(
1293:(
1287:t
1284:u
1281:o
1276:v
1269:)
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1260:(
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1248:o
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1199:.
1196:.
1193:.
1190:,
1187:1
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1181:0
1178:=
1175:n
1155:T
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1107:+
1104:s
1098:0
1088:=
1082:)
1079:s
1076:(
1070:n
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1056:)
1053:s
1050:(
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1038:o
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1026:=
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1020:s
1017:(
1014:H
991:)
988:s
985:(
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956:s
953:(
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930:s
927:(
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915:o
910:V
903:=
900:)
897:s
894:(
891:H
860:C
857:R
853:1
848:=
843:0
815:,
812:)
807:t
802:0
790:e
783:1
780:(
775:i
771:V
767:=
764:)
761:t
758:(
749:v
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698:)
695:t
692:(
683:v
651:t
645:d
634:v
627:d
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612:)
609:t
606:(
597:v
593:=
590:)
587:t
584:(
575:v
383:.
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117:(
112:)
108:(
98:·
91:·
84:·
77:·
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