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| In ], the reference value is usually the sampling frequency, denoted <math>f_s,\,</math> in '''samples per second''', because the frequency content of a sampled signal is completely defined by the content within a span of <math>f_s\,</math> ], at most. In other words, the frequency distribution is periodic with period <math>f_s.\,</math> When the actual frequency<math>, f,\,</math> has units of ] (] units), the normalized frequencies, also denoted by <math>f,\,</math> have units of '''cycles per sample''', and the periodicity of the normalized distribution is 1. And when the actual frequency<math>, \omega,\,</math> has units of radians per second (]), the normalized frequencies have units of '''radians per sample''', and the periodicity of the distribution is 2п. | In ], the reference value is usually the sampling frequency, denoted <math>f_s,\,</math> in '''samples per second''', because the frequency content of a sampled signal is completely defined by the content within a span of <math>f_s\,</math> ], at most. In other words, the frequency distribution is periodic with period <math>f_s.\,</math> When the actual frequency<math>, f,\,</math> has units of ] (] units), the normalized frequencies, also denoted by <math>f,\,</math> have units of '''cycles per sample''', and the periodicity of the normalized distribution is 1. And when the actual frequency<math>, \omega,\,</math> has units of radians per second (]), the normalized frequencies have units of '''radians per sample''', and the periodicity of the distribution is 2п. | ||
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In digital signal processing, the reference value is usually the sampling frequency, denoted in samples per second, because the frequency content of a sampled signal is completely defined by the content within a span of hertz, at most. In other words, the frequency distribution is periodic with period When the actual frequency has units of hertz (SI units), the normalized frequencies, also denoted by have units of cycles per sample, and the periodicity of the normalized distribution is 1. And when the actual frequency has units of radians per second (angular frequency), the normalized frequencies have units of radians per sample, and the periodicity of the distribution is 2п.
in samples per second, because the frequency content of a sampled signal is completely defined by the content within a span of 
When the actual frequency
has units of 
have units of cycles per sample, and the periodicity of the normalized distribution is 1. And when the actual frequency
has units of radians per second (If a sampled waveform is real-valued, such as a typical filter impulse response, the periodicity of the frequency distribution is still But due to symmetry, it is completely defined by the content within a span of just Accordingly, some filter design procedures/applications use that as the normalization reference (and the resulting units are half-cycles per sample). A filter design can be used at different sample-rates, resulting in different frequency responses. Normalization produces a distribution that is independent of the sample-rate. Thus one plot is sufficient for all possible sample-rates.
Accordingly, some filter design procedures/applications use that as the normalization reference (and the resulting units are half-cycles per sample). A filter design can be used at different sample-rates, resulting in different frequency responses. Normalization produces a distribution that is independent of the sample-rate. Thus one plot is sufficient for all possible sample-rates.
The following table shows examples of normalized frequencies for a 1 kHz signal, and a sample rate = 44.1 kHz.
= 44.1 kHz.
| Type | Computation | Value |
| Radians/sample | 2 pi 1000 / 44100 | 0.1425 |
| w.r.t. fs | 1000 / 44100 | 0.02676 |
| w.r.t. Nyquist | 1000 / 22050 | 0.04535 |