ABSTRACT
The concepts of Fourier transform, convolution, and window, discussed for functions on the continuous domain are readily adapted to the discrete case with one important stipulation that the spatial domain is discretized at a constant interval. Spectral analysis for infinite sequences can be developed without reference to a parent function from which the sequence is derived. One approach to the Fourier transform of an infinite sequence is to use the special case of the Fourier transform for continuous functions applied to the Dirac delta function. The concept of convolution carries over directly to the discrete domain from the continuous domain with an appropriate definition. Before investigating these assumptions and their effect on operations such as convolution, the Fourier transform is developed for the fourth fundamental type of function that is periodic and defined on a discrete domain, that is, a periodic sequence.
