# Homework Help: Fourier Transform Analysis

1. Jun 6, 2006

### Soilwork

Unfortunately I haven't really been able to find anything to help me on how to interpret fourier transforms and I need some help.

This is the question I am trying to do.

The superposition of two signals of the same amplitude but different frequencies and phase is responsible for the acoustic phenomenon of beats. If the two signals y1(t) and y2(t) are given by the expressions below:

y1(t)=$$Acos(\omega_1$$t-$$\phi_1)$$

and

y2(t)=$$Acos(\omega_2$$t-$$\phi_2)$$

Then the expression for the superposition is:

y = $$Acos(\frac{1} {2}(\omega_1-\omega_2)t+\frac{1} {2}(\phi_1-\phi_2))$$$$cos(\frac{1} {2}(\omega_1+\omega_2)t+\frac{1} {2}(\phi_1-\phi_2))$$

The file exam05final.txt contains 512 samples of just such a superposition sampled at 5.12 Hz. Your task is to determine as much as you can about the two signals, and if possible confirm your deductions

The first link below is the screenshot of the plot of the plain superposition signal. The second link below is the screenshot of the FFT output plot that I managed to get.
I guess the two peaks show the two frequencies that are within the superposition signal.