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);
  

A simple way to display the impulse response is with the Filter Visualization Tool (fvtool):

• fvtool(b,a)
  

Then click the Impulse Response button on the toolbar. This plot shows the exponential decay h(n) = 0.9n of the single pole system.:

Frequency Domain Filter Implementation

Frequency Response