Impulse Response

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

$$\delta (n)=\{\genfrac{}{}{0ex}{}{1,n=0,}{0,n\ne 0.}$$

You can generate an impulse sequence a number of ways; one straightforward way is

imp = [1; zeros(50,1)];

The impulse response of the simple filter with $$b=1$$ and $$a=[1-0.9]$$ is $$h(n)=0.9^n$$, which decays exponentially.

b = 1;
a = [1 -0.9];

h = filter(b,a,imp);

stem(0:50,h)

A simple way to display the impulse response is with the impz function.

impz(b,a,51)