# Nyquist frequency, Nyquist rate, digital signal processing time units, n, w, radians/sample. radians/second, Hertz etc.

It seems that DSP becomes confusing when you start, either reading about, or writing about, DSP quantities like filtering and modeling. Here is the scoop on this, to help if you need it.

First, Nyquist frequency and Nyquist rate: A band limited signal may be sampled by another signal (fs) that has a frequency two times the bandwidth ( B). B is called the Nyquist frequency and fs is called the Nyquist rate or simply the sample rate. Nyquist frequency is fs/2 if fs is twice B. These quantities can be normalized to fs = 1 ( normalized to fs) and the Nyquist frequency can be normalized to 0.5. ( Normalized to (fs/2)/fs.). Normalized Nyquist rate = 1. Normalized Nyquist frequency = 0.5. Samples/second. Some CAD tools use the Nyquist frequency as the normalization constant ( MATLAB filter design).

When the non normalized frequency is in terms of w, the angular frequency ( radians/second) and when this is normalized by the sample rate in samples/second the result is in radians/sample. Thus the normalized Nyquist frequency is pi radians/sample, and the normalized Nyquist rate is 2pi radians/sample.

There are also conversions available ( Wikipedia). f(radians/sample)=f(cycles/sec)*(2pi)/fs.

Please visit Signal Processing Group Inc. website for more technical info.