A typical choice of characteristic frequency is the
sampling rate (f_s) that is used to create the digital signal from a continuous one. The normalized quantity, f' = \tfrac{f}{f_s}, has the unit
cycle per sample regardless of whether the original signal is a function of time or distance. For example, when f is expressed in
Hz (
cycles per second), f_s is expressed in
samples per second. Some programs (such as
MATLAB toolboxes) that design filters with real-valued coefficients prefer the
Nyquist frequency (f_s/2) as the frequency reference, which changes the numeric range that represents frequencies of interest from \left[0, \tfrac{1}{2}\right]
cycle/sample to [0, 1]
half-cycle/sample. Therefore, the normalized frequency unit is important when converting normalized results into physical units. A common practice is to sample the frequency spectrum of the sampled data at frequency intervals of \tfrac{f_s}{N}, for some arbitrary integer N (see ). The samples (sometimes called frequency
bins) are numbered consecutively, corresponding to a frequency normalization by \tfrac{f_s}{N}. The normalized Nyquist frequency is \tfrac{N}{2} with the unit th
cycle/sample.
Angular frequency, denoted by \omega and with the unit
radians per second, can be similarly normalized. When \omega is normalized with reference to the sampling rate as \omega' = \tfrac{\omega}{f_s}, the normalized Nyquist angular frequency is . The following table shows examples of normalized frequency for f = 1
kHz, f_s = 44100
samples/second (often denoted by
44.1 kHz), and 4 normalization conventions: ==See also==