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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.
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 ...
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.
One way to do that is frequency-mixing the bandpass function down to the frequency range (0, B). 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 ...
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 .
A typical choice of characteristic frequency is the sampling rate that is used to create the digital signal from a continuous one. The normalized quantity, f ′ = f f s , {\displaystyle f'={\tfrac {f}{f_{s}}},} has the unit cycle per sample regardless of whether the original signal is a function of time or distance.
The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at four times that rate requires a sampling frequency of 800 Hz. This gives the anti-aliasing filter a transition band of 300 Hz ((f s /2) − B = (800 Hz/2) − 100 Hz = 300 Hz) instead of 0 Hz if the sampling frequency was 200 Hz. Achieving an ...
A lower value of n will also lead to a useful sampling rate. For example, using n = 4, the FM band spectrum fits easily between 1.5 and 2.0 times the sampling rate, for a sampling rate near 56 MHz (multiples of the Nyquist frequency being 28, 56, 84, 112, etc.). See the illustrations at the right.
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