DISCRETE FOURIER TRANSFORM (DFT)

Discrete Fourier Transform is carried out to overcome the limitation of Fourier series as well as DTFT. As length of signal increases, frequency spacing reduces, approximation error representation of spectrum decreases, resolution of spectrum increases, missing values in less point DFT are present in more point DFT. Ideally, the spectrum of DFT is discrete and also infinite but we calculate it only for one period of the signal values.For the same signal values with different periodic sequences,the output values of the bigger periodic sequences contains all the values of the output signal obtained from the smaller periodic sequences .Moreover,the values remain same for same period even if the number of samples increases.