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The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity for the class of functions that are band-limited to a given bandwidth, such that no actual information is lost in the sampling process. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions.
Fig 1: Typical example of Nyquist frequency and rate. They are rarely equal, because that would require over-sampling by a factor of 2 (i.e. 4 times the bandwidth). In signal processing, the Nyquist rate, named after Harry Nyquist, is a value equal to twice the highest frequency of a given function or signal
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 .
In the context of, for example, the sampling theorem and Nyquist sampling rate, bandwidth typically refers to baseband bandwidth. In the context of Nyquist symbol rate or Shannon-Hartley channel capacity for communication systems it refers to passband bandwidth. The Rayleigh bandwidth of a simple radar pulse is defined as the inverse of its ...
The Audio Engineering Society recommends 48 kHz sampling rate for most applications but gives recognition to 44.1 kHz for CD and other consumer uses, 32 kHz for transmission-related applications, and 96 kHz for higher bandwidth or relaxed anti-aliasing filtering. [10]
In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction and sample-rate reduction.
In signal processing, oversampling is the process of sampling a signal at a sampling frequency significantly higher than the Nyquist rate. Theoretically, a bandwidth-limited signal can be perfectly reconstructed if sampled at the Nyquist rate or above it. The Nyquist rate is defined as twice the bandwidth of the signal.
A bandlimited signal can be fully reconstructed from its samples, provided that the sampling rate exceeds twice the bandwidth of the signal. This minimum sampling rate is called the Nyquist rate associated with the Nyquist–Shannon sampling theorem.