DFT and FFT

DFT is a tool to study the signal in frequency domain.On the day of lab session we understood the logic and wrote the code for DFT. We tested it for some inputs and verified the output by analytical method. DFT assumes input as periodic and gives  periodic output sequence ,energy of the signal in time and frequency domain is equal.If we do zero padding then number of points increases hence resolution and quality of spectrum increases while the approximation error ,frequency spacing decreases.

We had to develop a program for FFT. During the lectures sir taught us how to find FFT for a 8 point sequence. So during pracs we had to complete FFT. Now as we knew the concept we were comfortable in building the algorithm. Implenting the flowgrapgh as it is in our code was difficult .The program was done , compiled and we got the results. It was observed that FFT is faster than DFT since it requires less no of real and complex additions and multiplications and also since FFT does the calculations parallely.