DFT and FFT

We performed DFT for 4 point as well as for 8 point .We understood the facts learnt in theory. It is very important to understand the working of the code.We performed DFT and Inverse DFT , Calculation of Energy for FFT and Inverse FFT .From this i understood that As the length of input signal increases:- (i) Frequency spacing decreases (ii) Approximation error in representation of spectrum decreases (iii) Resolution increases.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 decreaces.