Example 1

Since we are dealing with a sampled data digital frequency response,  ie of the form H(z), the actual frequency response will be based on some sampling frequency. For a sampling frequency of Fs Hz (1/T Hz), the frequency response is then considered between 0 and Fs/2.0. The sampling frequency is w = 2*pi radians or 1/T Hz.

So for N points, the resolution is Fs/(2*N) Hz/point.

For example, suppose we calculate the frequency response at 512 points using the FreqResponse method. Then suppose we have simulated data, sampled at 8kHz.:

    N = 512
    Fs = 8000 Hz 
    Frequency resolution = Fs/(2*N) = 8000/(2*512) = 7.8125 Hz/bin
    Max Freq = 512 x 7.8125 = 4000Hz.

Note that because we are estimating the frequency response directly from H(z) and can arbitrarily specify N, it is possible to obtain progressively finer resolutions as required.

Example 2

We have a transfer function which we would like to measure the frequency response characteristics of. Applying the FreqResponse method with N = 256, there is a peak in the 90th bin. Assuming Fs = 1000Hz, at what frequency does the maximum response occur?

f = 90*Fs/(2*N)
  = 90 * 1000/(2*256)
  = 175.7813 Hz

Frequency Resolution = Fs/(2*N) = 1000/(2*256) = 1.9531 Hz/point

Note

Using an FFT on the same example, we would have by comparison:

   N = 256
   Fs = 1000 Hz  ......Sampling frequency
   Delta_F = Fs ........Frequency resolution
                  = Fs/N = 1000/256 = 3.9063 Hz/bin
as shown previously.