Integer Sinusoidal Transforms

Abstract

Publisher Summary Sinusoidal transforms are transforms whose kernel elements are generated using sinusoidal functions. Sinusoidal transforms have excellent compression ability for image, thus, it have image coding as its major application. The kernel elements of sinusoidal transforms are the functions of sinusoidal functions, and so generally they are real numbers that are difficult or expensive to implement. This chapter explains the way integer sinusoidal transforms are generated and analyzes the integer cosine transform, which is probably the most important integer sinusoidal transform. It describes the two unified treatments of sinusoidal transforms proposed by Jain and Wang. Dyadic symmetry and its relation to the Walsh transform are given, whose results are used to generate integer sinusoidal transforms. As the discrete cosine transform plays a very important role in image coding, a detailed analysis of the integer cosine transform is also discussed in the chapter.