Normalized frequency (signal processing)
In digital signal processing (DSP), a normalized frequency is a ratio of a variable frequency (
) and a constant frequency associated with a system (such as a sampling rate,
Some software applications require normalized inputs and produce normalized outputs, which can be re-scaled to physical units when necessary.
Mathematical derivations are usually done in normalized units, relevant to a wide range of applications.
A typical choice of characteristic frequency is the sampling rate (
) that is used to create the digital signal from a continuous one.
has the unit cycle per sample regardless of whether the original signal is a function of time or distance.
[1] Some programs (such as MATLAB toolboxes) that design filters with real-valued coefficients prefer the Nyquist frequency
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
The samples (sometimes called frequency bins) are numbered consecutively, corresponding to a frequency normalization by
(16) [3] The normalized Nyquist frequency is
Angular frequency, denoted by
and with the unit radians per second, can be similarly normalized.
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
samples/second (often denoted by 44.1 kHz), and 4 normalization conventions:
