As indicated in Problem 5.53, there are many problems of practical importance in which o...

As indicated in Problem 5.53, there are many problems of practical importance in which one wishes to calculate the discrete Fourier transform (DFT) of discrete-time signals. Often, these signals are of quite long duration, and in such cases it is very important to use computationally efficient procedures. One of the reasons for the significant increase in the use of computerized techniques for the analysis of signals was the development of a very efficient technique known as the fast Fourier trans-form (FFT) algorithm for the calculation of the OFT of finite-duration sequences. In this problem, we develop the principle on which the FFT is based.