Discrete Fourier Transform

In the chapter, Discrete Fourier Transform, the most often used version of Fourier analysis, the DFT and its inverse are derived with appropriate examples. The DFT, as in all version of Fourier analysis, represents an arbitrary amplitude profile signal in terms of sinusoidal or equivalent complex exponentials. This transform is all important in practical signal and system analysis, since it approximates all other versions of Fourier analysis and has fast algorithms for its implementation. Further, it computes essential operations, such as convolution and correlation, faster than alternative methods. The criterion of representation of signals is the least squares error, which is practical with advantageous. The matrix formulation of the DFT is often used in its computation. The properties of the DFT are very useful in the analysis of signals, as in the case of all transforms. As in the case of the orthogonal transforms the power of a signal can be computed in its DFT representation also.