A duality theorem for the discrete sine transform (DST)

Abstract

This paper presents a new property called the Duality Theorem for the Discrete Sine Transform (DST). Discrete Sine Transform is a finite — length discrete transform which is related to the renowned Discrete Fourier Transform (DFT) and is quite popular in signal processing arena, but has remained in the oblivion from pure mathematicians. Many of the properties of the Discrete Sine Transform are akin to those of the Discrete Fourier Transform and Discrete Cosine Transform, subject to minor differences. A formal derivation of the Duality Theorem corresponding to the Discrete Sine Transform is given which was hitherto not mentioned or derived in the literature. The usage of Duality Theorem helps in finding the discrete time — domain function from the DST frequency domain and vice versa thereby reducing considerable labour involved in the evaluation of the summation and hence, saves computation time and cost of implementation to a considerable extent. DST finds applications in Image Processing, Signal Processing applications for Communication Systems, and in the numerical solutions of differential equations as well as partial differential equations of mathematics.