Linear Filtering and Filter Design (Image Processing Toolbox)

Image Processing Toolbox

Computing the Frequency Response of a Filter

The freqz2 function computes the frequency response for a two-dimensional filter. With no output arguments, freqz2 creates a mesh plot of the frequency response. For example, consider this FIR filter:

h =[0.1667    0.6667    0.1667
    0.6667   -3.3333    0.6667
    0.1667    0.6667    0.1667];

This command computes and displays the 64-by-64 point frequency response of h:

freqz2(h)

Figure 6-10: The Frequency Response of a Two-Dimensional Filter

To obtain the frequency response matrix H and the frequency point vectors f1 and f2, use output arguments:

[H,f1,f2] = freqz2(h);

freqz2 normalizes the frequencies f1 and f2 so that the value 1.0 corresponds to half the sampling frequency, or radians.

For a simple m-by-n response, as shown above, freqz2 uses the two-dimensional fast Fourier transform function fft2. You can also specify vectors of arbitrary frequency points, but in this case freqz2 uses a slower algorithm.

See Fourier Transform for more information about the fast Fourier transform and its application to linear filtering and filter design.

Creating the Desired Frequency Response Matrix Transforms