The goal of this project was to learn a little about the fourier transform operation and how to implement it programatically. The project has two implementations regarding the Fourier Transform one that is derived from the following formula:

and the other is an implmentation of the Fast Fourier Transform algorithm. The effiecency of the two algorithms is described as follows DFT => and FFT where n is the length of the input.

The input for this project I decided to be a .wav file. Provided a wav file the program parses the file extracting the necessary data and then converts it to a vector of complex double numbers. The FFT algorithm is designed in such a way that it can only run on data with a length that is a power of 2, so additional logic was added to pad the length of the data vector in the case that the data is not a power of 2.

Finally once the output vector is computed from the input vector I wrote a simple python program to graph the output on the x-y plane and one for magnitude-frequency. I realize that plotting the output on the Argand plane would be beter but it was outside the scope of the project. The graphs are presented once done and saved as png files in the project directory.