Z Transform Sinusoidal Response
Ele 541 Electronic Testing
Sinusoidal Response
Consider the response of a filter to the complex simusoidal signal x(k).
![](fimg1.gif)
The convolution summation describes the response
![](img5.gif)
Plugging in the sinusoidal input x(k)
![](fimg2.gif)
![](fimg3.gif)
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.
More information on
[Sequences and filters]
[Common Sequences ]
[Delay]
[Sinusoidal Response]