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The sampling frequency or sampling rate, , is the average number of samples obtained in one second, thus = /, with the unit samples per second, sometimes referred to as hertz, for example 48 kHz is 48,000 samples per second.
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 .
One of the possible reasons is to reduce the Nyquist rate for more efficient storage. And it turns out that one can directly achieve the same result by sampling the bandpass function at a sub-Nyquist sample-rate that is the smallest integer-sub-multiple of frequency A that meets the baseband Nyquist criterion: f s > 2B.
Sample-rate conversion prevents changes in speed and pitch that would otherwise occur when transferring recorded material between such systems. More specific types of resampling include: upsampling or upscaling; downsampling, downscaling, or decimation; and interpolation. The term multi-rate digital signal processing is sometimes used to refer ...
When is normalized with reference to the sampling rate as ′ =, the normalized Nyquist angular frequency is π radians/sample. The following table shows examples of normalized frequency for f = 1 {\displaystyle f=1} kHz , f s = 44100 {\displaystyle f_{s}=44100} samples/second (often denoted by 44.1 kHz ), and 4 normalization conventions:
Sampling rate conversion systems are used to change the sampling rate of a signal. The process of sampling rate decrease is called decimation, and the process of sampling rate increase is called interpolation. T. Schilcher. RF applications in digital signal processing//" Digital signal processing".
Sample rate Bit rate Bits per sample Latency CBR VBR Stereo Multichannel G.711: companding A-law or μ-law, PCM: 8 kHz 64 kbit/s 8 bit 125 μs (typical) Yes No No No G.711.0: Lossless compression of G.711: 8 kHz 0.2–65.6 kbit/s 8 bit 5–40 ms No Yes No No G.711.1: MDCT, A-law, μ-law: 8, 16 kHz 64, 80, 96 kbit/s 16 bit 11.875 ms Yes Yes No No
The selection of the sample rate was based primarily on the need to reproduce the audible frequency range of 20–20,000 Hz (20 kHz). The Nyquist–Shannon sampling theorem states that a sampling rate of more than twice the maximum frequency of the signal to be recorded is needed, resulting in a required rate of greater than 40 kHz.