Frequency response of discrete system

In the previous post, we discussed the impulse response. Impulse response h(n) is a digital system response in the time domain. But there is another characterization of the discrete system – frequency response H(e).

Frequency response can be calculated form impulse response by formula:

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

where |H(e)| – is amplitude frequency response

phase frequency response

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

First mentioned above – from impulse response;

Second – from discrete system equation:

Lets say we have digital filter described as:


then frequency response of digital filter would be:

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