ABSTRACT
This chapter develops a method of describing a signal in terms of a polynomial. Like the Fourier transform, the polynomial transform maps the operation of convolution into multiplication. Furthermore, the polynomial transform will provide a bridge between the continuous transform operations and the discrete transform. Signals can be represented in terms of polynomials. The chapter describes three ways of representing a signal — as a concept, as a polynomial, and as samples. The method of transforming from the coefficient representation to the sample representation is very simple. It is called evaluation. The opposite operation is the transformation from samples to coefficients. It is called as the interpolation. Interpolation transforms from the sample domain to the coefficient domain just as the Fourier transform transforms from the time to the frequency domain. The method for multiplying two polynomials is to multiply each element of the first polynomial times all of the elements of the second polynomial.
