The Karhunen-Loeve transform for a class of signals is proven to be a set of periodic sine functions and this Karhunen-Loeve series expansion can be obtained via an FFT algorithm. This fast algorithm obtained could be useful in data compression and other mean-square signal processing applications.

A fast Karhunen-Loeve transform for a class of random processes

Fast discrete sine transform algorithms

This chapter discusses the fast 1-D and 2-D DCT/DST algorithms for all even types of the discrete cosine transform (DCT) and discrete sine transform (DST). Almost all are direct algorithms defined by the recursive sparse matrix factorization of the transform matrix. DCTs and DSTs are members of the class of sinusoidal unitary transforms. A sinusoidal unitary transform is an invertible linear transform whose kernel is defined by a set of complete, orthogonal/orthonormal discrete cosine and/or sine basis functions. The fast 1-D DCT/DST algorithms are numerically stable, have the regular computational structures and employ real arithmetic only. The generalized signal flow graphs corresponding to the sparse matrix factorization of the transform matrix for the fast DCT/DST computation have also been provided in the chapter and they are ready to be used in practical applications.

Chapter 4 - Fast DCT/DST Algorithms

......................................................................................................................................... iv List of Figures ................................................................................................................................ ix List of Tables ................................................................................................................................ xi

Encoder complexity reduction with selective motion merge in hevc

Two major errors contained in the referred paper are pointed out. Reference of a new algorithm for the discrete sine transform is given.

Wang Zhongde

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