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The sample rate must exceed the Nyquist rate for the samples to suffice to represent (). The threshold / is called the Nyquist frequency and is an attribute of the sampling equipment. All meaningful frequency components of the properly sampled () exist below the Nyquist frequency.
For a given sampling rate (samples per second), the Nyquist frequency (cycles per second) is the frequency whose cycle-length (or period) is twice the interval between samples, thus 0.5 cycle/sample. For example, audio CDs have a sampling rate of 44100 samples/second. At 0.5 cycle/sample, the corresponding Nyquist frequency is 22050 cycles/second .
Nyquist's famous 1928 paper was a study on how many pulses (code elements) could be transmitted per second, and recovered, through a channel of limited bandwidth. [4] Signaling at the Nyquist rate meant putting as many code pulses through a telegraph channel as its bandwidth would allow.
In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by a communication channel (including responses of transmit and receive filters), result in no intersymbol interference or ISI. It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference.
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
Nyquist criterion may refer to: Nyquist stability criterion, a graphical technique for determining the stability of a feedback control system; Nyquist frequency, ½ of the sampling rate of a discrete signal processing system; Nyquist rate, a rate used in signal processing; Nyquist ISI criterion, a condition to avoid intersymbol interference
In particular, the theory, using signal processing language, is described in this 2009 paper. [4] They show, among other things, that if the frequency locations are unknown, then it is necessary to sample at least at twice the Nyquist criteria; in other words, you must pay at least a factor of 2 for not knowing the location of the spectrum .
In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass-filtered signal at a sample rate below its Nyquist rate (twice the upper cutoff frequency), but is still able to reconstruct the signal.