Discrete Fourier Transform

Abstract

The concept of signal conditioning holds true both for synthesis and analysis domain. When we are considering the discrete signal processing concept, the signal must be discrete both in time/ space domain and in frequency domain. But by Discrete Time Fourier Transform (DTFT), the discrete time signal is transformed into continuous frequency signal in analysis domain. Therefore, our objective should be to condition/ process the continuous periodic spectrum such that the spectrum can be used by discrete signal processors like computers and hand-held devices like mobile phones, directly. In the present chapter, we have first introduced the classical algorithm of Discrete Fourier Transform (DFT). A complete flow from analog continuous time signal to discrete spectrum analysis is represented. Next, a clockwise rotated phasor (twiddle factor) is presented to simplify the DFT algorithm. Some interesting observations related to the DFT operation both in electrical signal (1D) and image (2D) are also presented at the rear end of the chapter.