There has been a great deal of material in the area of discrete-time transforms that has been published in recent years. This book does an excellent job of presenting important aspects of such material in a clear manner. The book has 11 chapters and a very useful appendix. Seven of these chapters are essentially devoted to the Fourier series/transform, discrete Fourier transform, fast Fourier transform (FFT), and applications of the FFT in the area of spectral estimation. Chapters 8 through 10 deal with many other discrete-time transforms and algorithms to compute them. Of these transforms, the KarhunenLoeve, the discrete cosine, and the Walsh-Hadamard transform are perhaps the most well-known. A lucid discussion of number theoretic transforms i5 presented in Chapter 11. This reviewer feels that the authors have done a fine job of compiling the pertinent material and presenting it in a concise and clear manner. There are a number of problems at the end of each chapter, an appreciable number of which are challenging. The authors have included a comprehensive set of references at the end of the book. In brief, this book is a valuable contribution to the general areas of signal processing and communications. It can be used for a graduate level course in perhaps two ways. One would be to cover the first seven chapters in great detail. The other would be to cover the whole book by focussing on different topics in a selective manner. This book  by  Elliott  and Rao  is extremely  useful to researchers/engineers who are working  in the areas of signal processing and communications. It i s also an excellent reference book, and hence a valuable addition to one’s library

http://ieeexplore.ieee.org/iel5/5/31347/01457444.pdf

Multirate digital signal processing

Fractional Fourier transform as a signal processing tool: An overview of recent developments

Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography - however, this potential can only be achieved through the accurate, quantitative reconstruction of the power spectral density of real-world surfaces.

/pdf/quantitative-characterization-of-surface-topography-using-1di6n32wn5.pdf

Quantitative characterization of surface topography using spectral analysis

The problem of acoustic noise is becoming increasingly serious with the growing use of industrial and medical equipment, appliances, and consumer electronics. Active noise control (ANC), based on the principle of superposition, was developed in the early 20th century to help reduce noise. However, ANC is still not widely used owing to the effectiveness of control algorithms, and to the physical and economical constraints of practical applications. In this paper, we briefly introduce some fundamental ANC algorithms and theoretical analyses, and focus on recent advances on signal processing algorithms, implementation techniques, challenges for innovative applications, and open issues for further research and development of ANC systems.

/pdf/recent-advances-on-active-noise-control-open-issues-and-1wg2ydx57i.pdf

Recent Advances on Active Noise Control: Open Issues and Innovative Applications

https://www.dtc.umn.edu/s/resources/gg-se.pdf

A bibliography on nonlinear system identification

The discrete Hartley transform (DHT) is discussed as a tool for the processing of real signals. Fast Hartley transform (FHT) algorithms which compute the DHT in a time proportional to N log/sub 2/ N exist. In many applications, such as interpolation and convolution of signals, a significant number of zeros are padded to the nonzero valued samples before the transform is computed. It is shown that for such situations, significant savings in the number of additions and multiplications can be obtained by pruning the FHT algorithm. The modifications in the FHT algorithm as a result of pruning are developed and implemented in an FHT subroutine. The amount of savings in the operation is determined. >

Fast Hartley transform pruning

The Wigner-Ville distribution (WVD) is of great significance in time-frequency signal analysis. In the letter we present a new method to evaluate the WVD of a real signal using the fast Hartley transform (FHT). This is compared with the existing fast Fourier transform (FFT) method in terms of computation time. The FHT method presented turns out to be much faster than the FFT method.

New method of computing Wigner-Ville distribution

This paper attempts to analyze and classify the radar returns from a simulated ground based radar using Wigner-Ville distribution (WVD). Stochastic modeling methods like AR and ARMA have earlier been applied for the classification problem. However they suffer from inaccuracies such as showing inexact spectral widths, which is a prime factor to distinguish weather returns from birds, non-adaptability to time-varying clutter spectra, etc., despite being prominent in resolving spectral peaks. The paper proposes WVD as an alternative tool for the classification of radar returns, since it is a powerful technique for time-varying spectra. The analysis shows promising results especially from the view point of spectral widths, though faced with the problem of cross-spectral components. Examples of WVD applied to the simulated radar signal are presented to illustrate the advantages of this method.

Classification of radar returns using Wigner-Ville distribution

The least mean squared (LMS) algorithm and its variants have been the most often used algorithms in adaptive signal processing. However the LMS algorithm suffers from a high computational complexity, especially with large filter lengths. The Fourier transform-based block normalized LMS (FBNLMS) reduces the computation count by using the discrete Fourier transform (DFT) and exploiting the fast algorithms for implementing the DFT. Even though the savings achieved with the FBNLMS over the direct-LMS implementation are significant, the computational requirements of FBNLMS are still very high, rendering many real-time applications, like audio and video estimation, infeasible. The Hartley transform-based BNLMS (HBNLMS) is found to have a computational complexity much less than, and a memory requirement almost of the same order as, that of the FBNLMS. This paper is based on the cosine and sine symmetric implementation of the discrete Hartley transform (DHT), which is the key in reducing the computational complexity of the FBNLMS by 33% asymptotically (with respect to multiplications). The parallel implementation of the discrete cosine transform (DCT) in turn can lead to more efficient implementations of the HBNLMS.

/pdf/an-analysis-of-real-fourier-domain-based-adaptive-algorithms-4be7gdhyrr.pdf

An analysis of real-Fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

Two different window function families, namely, the first-order Bessel (I/sub 1/-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, are considered. Closed-form expressions are obtained which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc. Simple expressions relating to mainlobe width and maximum sidelobe level are given for the two families considered. The results are compared to those obtained by J.F. Kaiser and R.W. Schafer (1980) in the case of zeroth-order Bessel (I/sub 0/-sinh) family. >

K.M.M. Prabhu

Papers

Fast Hartley transform pruning

New method of computing Wigner-Ville distribution

Classification of radar returns using Wigner-Ville distribution

An analysis of real-Fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

Variable parameter window families for digital spectral analysis