In previous post we discussed about impulse response. Impulse response h(n) is digital system response in time domain. But there is another characterization of discrete system – frequency response H(e^{jω}).

Frequency response can be calculated form impulse response by formula:

This means frequency response is systems transfer coefficient to every frequency value. Frequency response is a complex function. So this can be evaluated as:

where |H(e^{jω})| – is amplitude frequency response

– phase frequency response.

There are two simple ways to calculate frequency response of discrete system:

First mentioned above – from impulse response;

Second – from discrete system equation:

Lets say we have digital filter described as:

y(n)=-a1·y(n-1)+b0·x(n)

then frequency response of digital filter would be: