Using a Fast Fourier Transform Algorithm

The symmetry and periodicity properties of the discrete Fourier transform (DFT) allow a variety of useful and interesting decompositions. In particular, by clever grouping and reordering of the complex exponential multiplications it is possible to achieve substantial computational savings while still obtaining the exact DFT solution (no approximation required). Many “fast” algorithms have been developed for computing the DFT, and collectively these are known as Fast Fourier Transform (FFT) algorithms. Always keep in mind that an FFT algorithm is not a different mathematical transform: it is simply an efficient means to compute the DFT. In this experiment you will use the Matlab fft() function to perform some frequency domain processing tasks.