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how to find equation for steady state

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thanglong

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Dear Friends:

I have a problem that I can't solve it. I need your help.

Problem:
A digital notch filter can be modeled by: y(n) + 0.90y(n-2) = x(n) + x(n-2)
where y(n) represents the filter output and x(n) is its input. the input sequence x(n) = 1+2cos(n*pi/2) is applied to this filter.

find the equation for the steady state output voltage Yss(n).
verify answer by using matlab.

Thanks a lot for your help.
 

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