Signals and Systems

11

Discrete Fourier Transform and Fast Fourier Transform

When both the time and the frequency variables are discrete, we use Discrete Fourier Transform (DFT). If x(n) represents the discrete time signal, X(ω) represents the discrete frequency transform function of x(n). The Fast Fourier Transform(FFT) is simply a class of special algorithms implementing the discrete Fourier transform and it saves considerable time in computation It is not a different transform from the DFT. It reduces considerable number of calculations of DFT. The aim of this chapter is to introduce DFT and FFT.