Frequency response of discrete system

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).

Frequency response can be calculated form impulse response by formula:

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

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

image006.gif – 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:

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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:

image010.gif

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