Determine the frequency response

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.

[Paul]

Hi Marina,

Do you know the math and just need help with implementation in code?

What have you tried so far?

[Marina Petani]

Hello! I know the math but not the implementation. i tried to create a dtft function but dont know how to solve this.

[Paul]

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]

function [H] = dtft(h,n,w)
H=h*exp(-j*n'*w);
end

[Paul]

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)