Mathematical Transforms Used for Multimedia Signal Processing

Abstract

The algorithms for multimedia data processing are mostly based and derived from the general signal processing techniques. They usually include standard transforms such as the Fourier transform, discrete cosine transform, and wavelets transform. Hence, in order to provide better understanding of algorithms in multimedia systems, the fundamental concepts of commonly used mathematical transforms have been considered and explained using several illustrative examples: the properties of the Fourier transform and analysis, discrete cosine transform, wavelets and multiresolution analysis. Additionally, in order to keep up with the advanced multimedia applications, time-frequency analysis and the Hermite projection/expansion method have been elaborated in details, as well. Therefore, this chapter aims to provide the necessary theoretical background on the mathematical transforms on the basic and advanced level.