There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes. The discussion includes nonstationary signal analysis, scale versus frequency, wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing. The main definitions and properties of wavelet transforms are covered, and connections among the various fields where results have been developed are shown. >

/pdf/wavelets-and-signal-processing-1gyx22a8e3.pdf

Wavelets and signal processing

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

From the Publisher:
Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is the first book to give a unified and coherent exposition of orthogonal signal decomposition techniques. Advances in the field of electrical engineering/computer science have occurred since the first edition was published in 1992. This second edition addresses new developments in applications-related chapters, especially in Chapter 4, "Filterbrook Families: Design and Performance," which is greatly expanded. Also included are the most recent applications of orthogonal transforms in digital communications and multimedia. 
Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is intended for graduate students and research and development practitioners engaged in signal processing applications in voice and image processing, multimedia, and telecommunications.

Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets

This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics.

/pdf/orthogonal-transmultiplexers-in-communication-a-review-4pb60c7nfc.pdf

Orthogonal transmultiplexers in communication: a review

The authors present an efficient, in-place algorithm for the batch processing of linear data arrays. These algorithms are efficient, easily scaled, and have no multiply operations. They are suitable as front-end filters for a bank of quadrature mirror filters and for pyramid coding of images. In the latter application, the binomial filter was used as the low-pass filter in pyramid coding of images and compared with the Gaussian filter devised by P.J. Burt (Comput. Graph. Image Processing, vol.16, p.20-51, 1981). The binomial filter yielded a slightly larger signal-to-noise ratio in every case tested. More significantly, for an (L+1)*(L+1) image array processed in (N+1)*(N+1) subblocks, the fast Burt algorithm requires a total of 2(L+1)/sup 2/N adds and 2(L+1)/sup 2/ (N/2+1) multiplies. The binomial algorithm requires 2L/sup 2/N adds and zero multiplies. >

A class of fast Gaussian binomial filters for speech and image processing

Full length article: Emerging applications of wavelets: A review

It has been shown that cyclostationarity in the received signal allows the receiver to blindly identify the channel impulse response using only second-order statistics. In orthogonal frequency-division multiplexing (OFDM) systems, cyclostationarity is embedded at the transmitter due to cyclic prefix. In this paper, a subspace approach based on second-order statistics is proposed for blind channel identification in OFDM systems. We derive a sufficient condition that guarantees all the channels to be identifiable no matter what their zero locations are. Computer simulations demonstrate the superior performance of the proposed algorithm over methods reported earlier in the literature.

Ali N. Akansu

Papers

Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets

Orthogonal transmultiplexers in communication: a review

A class of fast Gaussian binomial filters for speech and image processing

Full length article: Emerging applications of wavelets: A review

A subspace method for blind channel identification in OFDM systems