40:
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293:, such as those cited above, are all consistent with the definition presented in this article. Some later publications, including some respectable textbooks, call twice the signal bandwidth the Nyquist frequency; this is a distinctly minority usage, and the frequency at twice the signal bandwidth is otherwise commonly referred to as the
202:
represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample rate. The other three dots indicate the frequencies and amplitudes of three other sinusoids that would produce the same set of samples as the actual sinusoid that was sampled. Undersampling of the
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ahead of the sampler. Its job is to attenuate the frequencies above that limit. Finally, based on the characteristics of the filter, one chooses a sample rate (and corresponding
Nyquist frequency) that will provide an acceptably small amount of
43:
Typical example of
Nyquist frequency and rate. To avoid aliasing, the sampling rate must be no less than the Nyquist rate of the signal; that is, the Nyquist rate of the signal must be under double the Nyquist frequency of the
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In a typical application of sampling, one first chooses the highest frequency to be preserved and recreated, based on the expected content (voice, music, etc.) and desired fidelity. Then one inserts an
508:
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When the function domain is distance, as in an image sampling system, the sample rate might be dots per inch and the corresponding
Nyquist frequency would be in cycles per inch.
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143:. In applications where the sample rate is predetermined (such as the CD rate), the filter is chosen based on the Nyquist frequency, rather than vice versa.
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the existence of power in the continuous signal spectrum at frequencies higher than the
Nyquist frequency is the cause of aliasing error
253:). No matter what function we choose to change the amplitude vs frequency, the graph will exhibit symmetry between 0 and
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Frequencies "fold" around half the sampling frequency - which is why the frequency is often referred to as the folding frequency.
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234:) of the 4 dots if we were to adjust the frequency and amplitude of the sinusoid along the solid red segment (between
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is half the sampling rate and corresponds to the highest frequency which a sampled data system can reproduce without error.
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Digital Signal
Processing: Mathematical and Computational Methods, Software Development and Applications
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of amplitude varying with frequency. The dashed red lines are the corresponding paths of the aliases.
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The
Nyquist frequency is that frequency whose period is two sampling intervals.
118:) of a signal is less than the Nyquist frequency of the sampler, the resulting
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Paulo Sergio
Ramirez Diniz, Eduardo A. B. Da Silva, Sergio L. Netto (2002).
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107:). Conversely, the Nyquist rate for sampling a 22050 Hz signal is 44100
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Digital Signal
Processing Using MATLAB for Students and Researchers
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The black dots are aliases of each other. The solid red line is an
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is the corresponding
Nyquist frequency. The black dot plotted at
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Maximum frequency of non-aliased component upon sampling
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sequence is said to be free of the distortion known as
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227:, there would still be aliases at 0.6, 1.4, 1.6, etc.
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Digital Signal
Processing: System Analysis and Design
339:
Probability and Statistics: The Harald Cramér Volume
263: This symmetry is commonly referred to as
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404:. Princeton University Press. pp. 280–281.
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99:, the corresponding Nyquist frequency is 22050
398:James J. Condon & Scott M. Ransom (2016).
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378:is twice the bandwidth of the signal ... The
213:is what allows there to be a lower-frequency
533:: CS1 maint: multiple names: authors list (
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362:. John Wiley & Sons. p. 82.
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457:"An Introduction to Sampling Theory"
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277: (the Nyquist frequency) is
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616:Nyquist–Shannon sampling theorem
551:Nyquist–Shannon sampling theorem
455:Thomas Zawistowski; Paras Shah.
230:The red lines depict the paths (
702:Discrete-time Fourier transform
480:Jonathan M. Blackledge (2003).
513:. Cambridge University Press.
307:
217:. If the true frequency were
91:have a sampling rate of 44100
13:
1:
647:Statistical signal processing
320:
267:, and another name for
130:for that particular signal.
114:When the highest frequency (
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64:, is a characteristic of a
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832:
696:Discrete Fourier transform
673:Matched Z-transform method
178:is the sampling rate, and
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816:Digital signal processing
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690:Discrete cosine transform
655:
624:
593:
587:Digital signal processing
401:Essential Radio Astronomy
76:), the Nyquist frequency
723:Post's inversion formula
637:Digital image processing
425:Harry L. Stiltz (1961).
300:
32:Not to be confused with
632:Audio signal processing
289:Early uses of the term
486:. Horwood Publishing.
166:
87:. For example, audio
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356:John W. Leis (2011).
160:
42:
756:Anti-aliasing filter
685:Constant-Q transform
668:Advanced z-transform
136:anti-aliasing filter
428:Aerospace Telemetry
713:Integral transform
708:Impulse invariance
680:Bilinear transform
167:
74:samples per second
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803:
802:
728:Starred transform
718:Laplace transform
642:Speech processing
611:Estimation theory
431:. Prentice-Hall.
384:folding frequency
380:Nyquist frequency
291:Nyquist frequency
279:folding frequency
244: and
169:In this example,
147:Folding frequency
80:cycles per second
58:folding frequency
54:Nyquist frequency
50:signal processing
16:(Redirected from
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601:Detection theory
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151:Main article:
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109:samples/second
93:samples/second
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733:Zak transform
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70:sampling rate
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62:Harry Nyquist
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18:Nyquist limit
780:Quantization
775:Oversampling
769:
766:Nyquist rate
761:Downsampling
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460:. Retrieved
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376:Nyquist rate
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295:Nyquist rate
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203:sinusoid at
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128:Nyquist rate
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34:Nyquist rate
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663:Z-transform
795:Upsampling
656:Techniques
625:Sub-fields
321:References
770:frequency
529:cite book
342:. Wiley.
116:bandwidth
44:sampling.
810:Category
751:Aliasing
743:Sampling
545:See also
462:17 April
336:(1959).
153:Aliasing
141:aliasing
124:aliasing
265:folding
163:example
66:sampler
704:(DTFT)
594:Theory
517:
490:
435:
408:
366:
95:. At
52:, the
698:(DFT)
692:(DCT)
301:Notes
215:alias
535:link
515:ISBN
488:ISBN
464:2010
433:ISBN
406:ISBN
374:The
364:ISBN
232:loci
219:0.4
205:0.6
194:0.6
180:0.5
56:(or
382:or
111:.
89:CDs
48:In
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768:/
531:}}
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184:Ă—
105:Hz
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