Discrete Cosine and Sine Transforms: General Properties, Fast Algorithms and Integer Approximations

Since the book, "Discrete Cosine Transform" by K. R. Rao and P. Yip, (Academic Press, Boston) was published in 1990, the DCT has increasingly attracted the attention of scientific, engineering and research communities. The DCT is used in many applications and in data compression in particular. This is due to the fact that the DCT has excellent energy-packing capability and also approaches the statistically optimal Karhunen-LoшЕ? transform (KLT) in decorrrelating a signal. The development of various fast algorithms for the efficient implementation of the DCT involving real arithmetic only, further contributed to its popularity. In the last several years there have been significant advances and developments in both theory and applications relating to transform processing of signals. In particular, digital processing motivated the investigation of other forms of discrete cosine transforms (DCTs) for their integer approximations. International standards organizations (ISO/IEC and ITU-T) have adopted the use of various forms of the integer DCT. At the same time, the investigation of other forms of discrete sine transforms (DSTs) has made a similar impact. There is therefore a need to extend the coverage to include these techniques. This book is aimed at doing just that.