# Integration in Frequency Domain

1. Oct 6, 2015

### yukari1310

How to integrate $$\int_{-0.5}^{0.5} {\bigg({\frac{1}{4-2e^{-j2{\pi}f}}}\bigg)}^2 df$$

2. Oct 6, 2015

### BvU

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Hello again; must be you forgot how PF homework sections work: you are supposed to make an effort yourself.
In the mean time I do wonder where this comes from and what the problem statement really is: you now seem to be wanting to integrate a complex function over a section of the real axis ?

3. Oct 6, 2015

### yukari1310

I did try it somewhere else using integration by parts but the function to be integrate just got more complicated as I go on.
I am suppose to find the energy signal of a DTFT [ie X(f)] signal. The range defined is over the principal period of the DTFT signal.

4. Oct 6, 2015

### BvU

Isn't the energy a real number ?

5. Oct 6, 2015

### yukari1310

Yeah? So can you give me some hints on how to integrate the complex function?

6. Oct 6, 2015

### HallsofIvy

Staff Emeritus
I would think a rather obvious substitution would be $u= 4- 2e^{j2\pi f}$. Did you try that? What do you get?

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