In this book we design some high-performance and low-complexity filter banks for multimedia compression and digital communications. We first present a systematic design of the fast approximation of the Discrete Cosine Transform (DCT) using the lifting scheme. A family of fast lapped transforms is then developed, using time-domain pre- and post-processing of the DCT. Compared to the wavelet-based JPEG 2000 standard, our method achieves similar performance with lower complexity. It has been applied into Microsoft/SMPTE VC-1 and JPEG XR standards. Several generalizations are developed next. First, we propose a general structure for linear-phase paraunitary filter banks that employs multiple stages of pre- and post-processing of the DCT. Secondly, we investigate the optimal pre- and post-processing for wavelet-based image and video compression. We then introduce an efficient structure for oversampled linear-phase filter banks. Finally, the application of oversampled filter bank in channel equalization is investigated, and a modified Orthogonal Frequency Division Multiplexing (OFDM) scheme is proposed.
