The impulse response of a digital filter is the output arising from the unit impulse sequence defined as
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 with and is , which decays exponentially.
b = 1; a = [1 -0.9]; h = filter(b,a,imp); stem(0:49,h)
A simple way to display the impulse response is with the Filter Visualization Tool, fvtool.
Click the Impulse Response button, , on the toolbar, select Analysis > Impulse Response from the menu, or type the following code to obtain the exponential decay of the single-pole system.