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Sample-rate conversion, sampling-frequency conversion or resampling is the process of changing the sampling rate or sampling frequency of a discrete signal to obtain a new discrete representation of the underlying continuous signal. [1]
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.
The Nyquist–Shannon sampling theorem implies that a faithful reproduction of the original signal is only possible if the sampling rate is higher than twice the highest frequency of the signal. Since a practical ADC cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter ...
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.
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.
Similarly, the accuracy of the sampling timing, or aperture uncertainty of the sampler, frequently the analog-to-digital converter, must be appropriate for the frequencies being sampled 108MHz, not the lower sample rate. If the sampling theorem is interpreted as requiring twice the highest frequency, then the required sampling rate would be ...