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

In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

Multiple criteria decision making

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

The New Encyclopaedia Britannica

The problem of noise reduction has attracted a considerable amount of research attention over the past several decades. Among the numerous techniques that were developed, the optimal Wiener filter can be considered as one of the most fundamental noise reduction approaches, which has been delineated in different forms and adopted in various applications. Although it is not a secret that the Wiener filter may cause some detrimental effects to the speech signal (appreciable or even significant degradation in quality or intelligibility), few efforts have been reported to show the inherent relationship between noise reduction and speech distortion. By defining a speech-distortion index to measure the degree to which the speech signal is deformed and two noise-reduction factors to quantify the amount of noise being attenuated, this paper studies the quantitative performance behavior of the Wiener filter in the context of noise reduction. We show that in the single-channel case the a posteriori signal-to-noise ratio (SNR) (defined after the Wiener filter) is greater than or equal to the a priori SNR (defined before the Wiener filter), indicating that the Wiener filter is always able to achieve noise reduction. However, the amount of noise reduction is in general proportional to the amount of speech degradation. This may seem discouraging as we always expect an algorithm to have maximal noise reduction without much speech distortion. Fortunately, we show that speech distortion can be better managed in three different ways. If we have some a priori knowledge (such as the linear prediction coefficients) of the clean speech signal, this a priori knowledge can be exploited to achieve noise reduction while maintaining a low level of speech distortion. When no a priori knowledge is available, we can still achieve a better control of noise reduction and speech distortion by properly manipulating the Wiener filter, resulting in a suboptimal Wiener filter. In case that we have multiple microphone sensors, the multiple observations of the speech signal can be used to reduce noise with less or even no speech distortion

/pdf/new-insights-into-the-noise-reduction-wiener-filter-5fsg66xg9i.pdf

New insights into the noise reduction Wiener filter

This paper presents a new method for the design of oversampled uniform DFT-filter banks for the special application of subband adaptive beamforming with microphone arrays. Since array applications rely on the fact that different source positions give rise to different signal delays, a beamformer alters the phase information of the signals. This in turn leads to signal degradations when perfect reconstruction filter banks are used for the subband decomposition and reconstruction. The objective of the filter bank design is to minimize the magnitude of all aliasing components individually, such that aliasing distortion is minimized although phase alterations occur in the subbands. The proposed method is evaluated in a car hands-free mobile telephony environment and the results show that the proposed method offers better performance regarding suppression levels of disturbing signals and much less distortion to the source speech.

/pdf/filter-bank-design-for-subband-adaptive-microphone-arrays-czizhx0cs8.pdf

Filter bank design for subband adaptive microphone arrays

This paper discusses a multirate filterbank-based extended infomax algorithm for real-world signal separation, i.e., convolved mixtures separation. Since convolution in the time domain corresponds to instantaneous mixing in the frequency domain, polyphase subband projection naturally becomes an efficient alternative to the Fourier transform based frequency domain approach. The online implementation proposed is featured by a simultaneous inverse channel identification in the frequency domain and signal filtering in the time domain. It is shown that an over-representation structure reduces aliasing between different bands and results in more accurate inverse channel estimates. Therefore, it provides better performance than the Fourier transform based structure in the measures of both separation and distortion. The performance limitation of the method is also evaluated in terms of the Wiener solution.

Blind signal separation using overcomplete subband representation

This paper introduces a new constrained adaptive subband beamformer algorithm for speech enhancement in acoustic telecommunication systems. The solution relies on a pre-calculated source covariance matrix and recursive estimates of background noise- and handsfree signal covariance matrices. The constraint acts as an eye-opening in a vicinity of the near-field location of the source and degradations from steering-vector errors can therefor be made small. The algorithm is applied in subbands using a uniform multi channel over-sampled filterbank. Simulations with real speech recorded in an automobile hands-free environment show 19 dB noise reduction and 20 dB hands-free suppression.

/pdf/soft-constrained-subband-beamforming-for-hands-free-speech-323ru9n9ca.pdf

Soft constrained subband beamforming for hands-free speech enhancement

Subband adaptive filters have been proposed to avoid the drawbacks of slow convergence and high computational complexity associated with time domain adaptive filters. Subband processing introduces transmission delays caused by the filter bank and signal degradations due to aliasing effects. One efficient way to reduce the aliasing effects is to allow a higher sample rate than critically needed in the subbands and thus reduce subband signal degradation. We suggest a design method, for uniform DFT filter banks with any oversampling factor, where the total filter bank group delay may be specified, and where the aliasing and magnitude/phase distortions are minimized.

/pdf/design-of-oversampled-uniform-dft-filter-banks-with-delay-3pfxbdle7f.pdf

Design of oversampled uniform DFT filter banks with delay specification using quadratic optimization

http://bth.diva-portal.org/smash/get/diva2:835181/FULLTEXT01

Nedelko Grbic

Papers

Filter bank design for subband adaptive microphone arrays

Blind signal separation using overcomplete subband representation

Soft constrained subband beamforming for hands-free speech enhancement

Design of oversampled uniform DFT filter banks with delay specification using quadratic optimization

Source localization for multiple speech sources using low complexity non-parametric source separation and clustering