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Real world signals are not strictly bandlimited, and signals of interest typically have unwanted energy outside of the band of interest. Because of this, sampling functions and digital signal processing functions which change sample rates usually require bandlimiting filters to control the amount of
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One important consequence of this result is that it is impossible to generate a truly bandlimited signal in any real-world situation, because a bandlimited signal would require infinite time to transmit. All real-world signals are, by necessity,
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is, strictly speaking, a signal with zero energy outside of a defined frequency range. In practice, a signal is considered bandlimited if its energy outside of a frequency range is low enough to be considered negligible in a given application.
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be bandlimited. Nevertheless, the concept of a bandlimited signal is a useful idealization for theoretical and analytical purposes. Furthermore, it is possible to approximate a bandlimited signal to any arbitrary level of accuracy desired.
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representation of a signal, but if a finite number of
Fourier series terms can be calculated from that signal, that signal is considered to be band-limited. In mathematic terminology, a bandlimited signal has a
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completely from these samples. Similarly, sums of sinusoids with different frequencies and phases are also bandlimited to the highest of their frequencies.
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has intervals full of zeros, because points in such intervals are not isolated. Thus the only time- and bandwidth-limited signal is a constant zero.
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or twice the highest frequency component in the signal, as shown in the figure. According to the sampling theorem, it is possible to reconstruct
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distortion. Bandlimiting filters should be designed carefully to manage other distortions because they alter the signal of interest in both its
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Assume that a signal f(t) which has finite support in both domains and is not identically zero exists. Let's sample it faster than the
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A bandlimited signal cannot be also timelimited. More precisely, a function and its
Fourier transform cannot both have finite
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unless it is identically zero. This fact can be proved using complex analysis and properties of the
Fourier transform.
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is a sum of trigonometric functions, and since f(t) is time-limited, this sum will be finite, so
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The signal whose
Fourier transform is shown in the figure is also bandlimited. Suppose
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A bandlimited signal can be fully reconstructed from its samples, provided that the
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the magnitude of which is shown in the figure. The highest frequency component in
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The reconstruction of a signal from its samples can be accomplished using the
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and communications. Examples include controlling interference between
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is the frequency used for discretization. If f is bandlimited,
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In general, infinitely many terms are required in a continuous
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is a (suitably chosen) measure of time duration (in seconds).
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An example of a simple deterministic bandlimited signal is a
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it by defining technical terminology, and by adding examples.
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is zero outside of a certain interval, so with large enough
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is a (suitably chosen) measure of bandwidth (in hertz), and
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all zeros of non-constant holomorphic function are isolated
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Bandlimiting is an essential part of many applications in
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Limiting a signal to contain only low-frequency components
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of the signal. This minimum sampling rate is called the
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in frequency also forms the mathematical basis for the
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will be zero in some intervals too, since individual
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A similar relationship between duration in time and
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may be too technical for most readers to understand
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141:This article may be written in a style that is
1108:Fourier transform § Uncertainty principle
1513:won't overlap. According to DTFT definition,
1767:time–frequency resolution one may achieve.
608:{\displaystyle f_{s}={\tfrac {1}{T}}>2f}
557:{\displaystyle x(t)=\sin(2\pi ft+\theta ).}
428:A bandlimited signal may be either random (
66:Learn how and when to remove these messages
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890:completely and exactly using the samples
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350:Learn how and when to remove this message
332:Learn how and when to remove this message
262:Learn how and when to remove this message
116:Learn how and when to remove this message
100:, without removing the technical details.
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1084:{\displaystyle f_{s}>R_{N}\,}
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1798:. Cambridge, MA: MIT Press.
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848:{\displaystyle R_{N}=2B\,}
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1813:Digital signal processing
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470:Nyquist rate
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405:bandlimited
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363:Bandlimiting
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322:January 2011
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308:Please help
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252:January 2011
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194:Please help
189:verification
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143:too abstract
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106:January 2013
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18:Band-limited
1759:Gabor limit
1612:timelimited
1047:as long as
490:time domain
314:introducing
1788:References
1486:in sum of
430:stochastic
222:newspapers
52:improve it
1669:≥
1624:bandwidth
1298:∞
1290:∞
1287:−
1277:∑
546:θ
534:π
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466:bandwidth
161:June 2015
58:talk page
1807:Category
1771:See also
1636:variance
1457:supports
1347:, where
497:sinusoid
482:aliasing
407:baseband
390:sampling
386:aliasing
1114:support
450:support
310:improve
236:scholar
153:improve
151:Please
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1687:where
1616:cannot
1120:Proof:
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243:JSTOR
229:books
1183:and
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1752:In
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