Help me find frequency response for this system

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qmriso

qmriso

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Can somebody help me to find frequency response for the system
Code:
h(n) = (a)^n*cos(n*pi)*u(n)
 

Re: frequency response

h(n) = (a)^n*cos(n*pi)*u(n)

I think u can use the Multiplication properity of the discreate time fourier transform
which is " Multiplication on time domain is a convolution in frequency domain"

so if u have function
h(n)=x(n)y(n) ---->DTFT----> H(e^jw)=1/(2pi)int(X(e^jw)Y(e^j(w-m))dm,0,2pi)

so in ur problem let x(n)=(a)^n*u(n) & y(n)=cos(n*pi)

then get the DTFT of y(n) , x(n)

from FT tabels get X(e^jw),Y(e^jw) as following

X(e^jw)=1/(1-a*e^(-jw)) Y(e^jw)=pi*sum(d(w-pi-2*pi*l)+d(w+pi-2*pi*l),l=-inf,l=inf)

Then get the convolution between them


I hope that help
 

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