trouble computing the DFT of x[n] = sin(pi*n/4),

[DFT]

DTF

hi,

I'm having a lot of trouble computing the DFT of x[n] = sin(pi*n/4),

Computing the output of LTI system to the IP response of

H(ω) = (1 +EXP^-j2Π*ω)/(1 +½EXP^-j4Π*ω)

What is Y(ω)?

I would really appreciate if someone could help me solve this Question so I can attempt other question of a similar manner.

Thank you in advance

 

[Aya2002]

DTF

can u please explain more?

 

[DFT]

Re: DTF

Basically you have a LTI system

Input
x[n] = sin(pi*n/4)

Frequency Response

H(ω) = (1 +EXP^-j2Π*ω)/(1 +½EXP^-j4Π*ω)

First find X(ω)
Second find Y(ω)

then find

y[n]




Thank you