First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book.

Wavelets and Subband Coding

A new algorithm is introduced for the 2m-point discrete cosine transform. This algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms, and it makes the system simpler.

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A new algorithm to compute the discrete cosine Transform

Many advanced video applications require manipulations of compressed video signals. Popular video manipulation functions include overlap (opaque or semitransparent), translation, scaling, linear filtering, rotation, and pixel multiplication. We propose algorithms to manipulate compressed video in the compressed domain. Specifically, we focus on compression algorithms using the discrete cosine transform (DCT) with or without motion compensation (MC). Such compression systems include JPEG, motion JPEG, MPEG, and H.261. We derive a complete set of algorithms for all aforementioned manipulation functions in the transform domain, in which video signals are represented by quantized transform coefficients. Due to a much lower data rate and the elimination of decompression/compression conversion, the transform-domain approach has great potential in reducing the computational complexity. The actual computational speedup depends on the specific manipulation functions and the compression characteristics of the input video, such as the compression rate and the nonzero motion vector percentage. The proposed techniques can be applied to general orthogonal transforms, such as the discrete trigonometric transform. For compression systems incorporating MC (such as MPEG), we propose a new decoding algorithm to reconstruct the video in the transform domain and then perform the desired manipulations in the transform domain. The same technique can be applied to efficient video transcoding (e.g., from MPEG to JPEG) with minimal decoding. >

Manipulation and compositing of MC-DCT compressed video

The discrete cosine transform (DCT) is widely applied in various fields, including image data compression, because it operates like the Karhunen-Loeve transform for stationary random data. This paper presents a recursive algorithm for DCT with a structure that allows the generation of the next higher order DCT from two identical lower order DCT's. As a result, the method for implementing this recursive DCT requires fewer multipliers and adders than other DCT algorithms.

A fast recursive algorithm for computing the discrete cosine transform

Several fast algorithms for computing discrete cosine transforms (DCTs) and their inverses on multidimensional inputs of sizes which are powers of 2 are introduced. Because the 1-D 8-point DCT and the 2-D 8*8-point DCT are so widely used, they are discussed in detail. Algorithms for computing scaled DCTs and their inverses are also presented. These have applications in compression of continuous tone image data, where the DCT is generally followed by scaling and quantization. >

Fast algorithms for the discrete cosine transform

An N -point discrete Fourier transform (DFT) algorithm can be used to evaluate a discrete cosine transform by a simple rearrangement of the input data. This method is about two times faster compared to the conventional method which uses a 2N -point DFT.

On the Computation of the Discrete Cosine Transform

A technique for constructing an N-input concentrator from two (N/2)-input concentrators and a stage of 2/spl times/2 switching elements is described. Recursive decomposition of each of the (N/2)-input concentrators yields a log/sub 2/N-stage switching network similar in topology to the inverse omega network. The control algorithm for setting the switching elements is shown to be a simple logic function of the activity bits of the inputs. An iterative cell that combines the functions of the control logic and the 2/spl times/2 switching element can be used as a building block to realize the entire concentrator. Applications of the concentrator structure as an interconnection fabric in fast packet switching is explored. This leads to an efficient self-routing network, similar in topology to the transposed Batcher-banyan network. >

A recursive concentrator structure with applications to self-routing switching networks

It is shown that the nonblocking property of reverse banyan networks mentioned in the above paper follows directly from the fact that banyan networks can realize permutations characterized by bitonic sequences. >

M.J. Narasimha

Papers

On the Computation of the Discrete Cosine Transform

A recursive concentrator structure with applications to self-routing switching networks

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