Sinusoidal Response
Consider the response of a filter to the complex simusoidal signal x(k).
The convolution summation describes the response
Plugging in the sinusoidal input x(k)
where
is H(z), the z-transform of h(k) with
. Therefore letting in
the unit pulse response of a filter, H(z), allows
us to evaluate the sinusoidal response of the filter.
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