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I've reduced my problem to $H(w) = \dfrac{1}{(1-\frac{1}{4}e^{-jw})(1-\frac{1}{3}e^{-jw})}$. I need its inverse discrete Fourier transform.

My thinking is that I could use partial fraction decomposition to break this into two fractions of the form $\dfrac{1}{(1-ae^{-jw})}$ which I can then inverse Fourier transform to get a result of the form $h[n] = a^nu[n]$

My question is in two parts:

1: is this a good method to get the inverse discrete Fourier transform of H?

2: if not what should I do? Is there a simpler solution?

3: if so, how would I decompose H into two fractions?

Daniel B.
  • 601

1 Answers1

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Now that I've had some time away from the problem I realize I was over-thinking this quite badly ... There is no need to do any kind of logs or anything. To simplify, I let $S = e^{-jw}$

Thus $H(w) = \dfrac{1}{(1-\frac{1}{4}e^{-jw})(1-\frac{1}{3}e^{-jw})}$ becomes $H(w) = \dfrac{1}{(1-\frac{1}{4}S)(1-\frac{1}{3}S)}$

Which I solved in the usual way.

Daniel B.
  • 601