Signal Processing Toolbox

Impulse Response

The impulse response of a digital filter is the output arising from the unit impulse input sequence defined as

In MATLAB, you can generate an impulse sequence a number of ways; one straightforward way is

imp = [1; zeros(49,1)];

The impulse response of the simple filter b = 1 and a = [1 -0.9] is

h = filter(b,a,imp);

The impz function in the toolbox simplifies this operation, choosing the number of points to generate and then making a stem plot (using the stem function).

impz(b,a)

The plot shows the exponential decay h(n) = 0.9n of the single pole system.

Frequency Domain Filter Implementation

Frequency Response