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.
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