Determine the frequency response

2022 6 5
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更新时间：2022 6 5
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Its given:
ℎ(n)={(0.95)^n cos(2𝜋0.066n) + (0.75)^n cos(2𝜋0.172n) + (0.6)^n cos(2𝜋0.241n)} 𝑢(n)
Find: |H(e^jw)| if w = 0, w = pi/2, w = pi.
Draw the graph of |H(e^jw)| if 0 < w < pi
Also find the phase spectrum.

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Paul
Paul 2022-6-5
编辑：Paul 2022-6-5
Hi Marina,
Do you know the math and just need help with implementation in code?
What have you tried so far?
Marina Petani
Marina Petani 2022-6-5
Hello! I know the math but not the implementation. i tried to create a dtft function but dont know how to solve this.
Paul
Paul 2022-6-5
If you show your code, you're more likely to get help.
If you are trying to use a DTFT-based approximation, you don't need to write your own function. freqz can be used to compute the DTFT of a finite duration sequence. Of course, h[n] is infinite duration, but I assume your DTFT function is assuming that there is some value N for which h[n] = 0 for n > N.
Marina Petani
Marina Petani 2022-6-5
function [H] = dtft(h,n,w)
H=h*exp(-j*n'*w);
end
Paul
Paul 2022-6-5
The DTFT is a sum over n, so you'll either
a) use the sum function combined with element wise multiplication times, .*
or
b) use a loop over n to sum up h(n)*exp(-1j*n*w)

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