This book is devoted to the study of the problem of speech enhancement whose objective is the recovery of a signal of interest (i.e., speech) from noisy observations. Typically, the recovery process is accomplished by passing the noisy observations through a linear filter (or a linear transformation). Since both the desired speech and undesired noise are filtered at the same time, the most critical issue of speech enhancement resides in how to design a proper optimal filter that can fully take advantage of the difference between the speech and noise statistics to mitigate the noise effect as much as possible while maintaining the speech perception identical to its original form. The optimal filters can be designed either in the time domain or in a transform space. As the title indicates, this book will focus on developing and analyzing optimal filters in the Karhunen-Loève expansion (KLE) domain. We begin by describing the basic problem of speech enhancement and the fundamental principles to solve it in the time domain. We then explain how the problem can be equivalently formulated in the KLE domain. Next, we divide the general problem in the KLE domain into four groups, depending on whether interframe and interband information is accounted for, leading to four linear models for speech enhancement in the KLE domain. For each model, we introduce signal processing measures to quantify the performance of speech enhancement, discuss the formation of different cost functions, and address the optimization of these cost functions for the derivation of different optimal filters. Both theoretical analysis and experiments will be provided to study the performance of these filters and the links between the KLE-domain and time-domain optimal filters will be examined. Table of Contents: Introduction / Problem Formulation / Optimal Filters in the Time Domain / Linear Models for Signal Enhancement in the KLE Domain / Optimal Filters in the KLE Domain with Model 1 / Optimal Filters in the KLE Domain with Model 2 / Optimal Filters in the KLE Domain with Model 3 / Optimal Filters in the KLE Domain with Model 4 / Experimental Study

This book is devoted to the study of the problem of speech enhancement whose objective is the recovery of a signal of interest (i.e., speech) from noisy observations. Typically, the recovery process is accomplished by passing the noisy observations through a linear filter (or a linear transformation). Since both the desired speech and undesired noise are filtered at the same time, the most critical issue of speech enhancement resides in how to design a proper optimal filter that can fully take advantage of the difference between the speech and noise statistics to mitigate the noise effect as much as possible while maintaining the speech perception identical to its original form. The optimal filters can be designed either in the time domain or in a transform space. As the title indicates, this book will focus on developing and analyzing optimal filters in the Karhunen-Loève expansion (KLE) domain. We begin by describing the basic problem of speech enhancement and the fundamental principles to solve it in the time domain. We then explain how the problem can be equivalently formulated in the KLE domain. Next, we divide the general problem in the KLE domain into four groups, depending on whether interframe and interband information is accounted for, leading to four linear models for speech enhancement in the KLE domain. For each model, we introduce signal processing measures to quantify the performance of speech enhancement, discuss the formation of different cost functions, and address the optimization of these cost functions for the derivation of different optimal filters. Both theoretical analysis and experiments will be provided to study the performance of these filters and the links between the KLE-domain and time-domain optimal filters will be examined. Table of Contents: Introduction / Problem Formulation / Optimal Filters in the Time Domain / Linear Models for Signal Enhancement in the KLE Domain / Optimal Filters in the KLE Domain with Model 1 / Optimal Filters in the KLE Domain with Model 2 / Optimal Filters in the KLE Domain with Model 3 / Optimal Filters in the KLE Domain with Model 4 / Experimental Study

This book focuses on a class of single-channel noise reduction methods that are performed in the frequency domain via the short-time Fourier transform (STFT). The simplicity and relative effectiveness of this class of approaches make them the dominant choice in practical systems. Even though many popular algorithms have been proposed through more than four decades of continuous research, there are a number of critical areas where our understanding and capabilities still remain quite rudimentary, especially with respect to the relationship between noise reduction and speech distortion. All existing frequency-domain algorithms, no matter how they are developed, have one feature in common: the solution is eventually expressed as a gain function applied to the STFT of the noisy signal only in the current frame. As a result, the narrowband signal-to-noise ratio (SNR) cannot be improved, and any gains achieved in noise reduction on the fullband basis come with a price to pay, which is speech distortion. In this book, we present a new perspective on the problem by exploiting the difference between speech and typical noise in circularity and interframe self-correlation, which were ignored in the past. By gathering the STFT of the microphone signal of the current frame, its complex conjugate, and the STFTs in the previous frames, we construct several new, multiple-observation signal models similar to a microphone array system: there are multiple noisy speech observations, and their speech components are correlated but not completely coherent while their noise components are presumably uncorrelated. Therefore, the multichannel Wiener filter and the minimum variance distortionless response (MVDR) filter that were usually associated with microphone arrays will be developed for single-channel noise reduction in this book. This might instigate a paradigm shift geared toward speech distortionless noise reduction techniques. Table of Contents: Introduction / Problem Formulation / Performance Measures / Linear and Widely Linear Models / Optimal Filters with Model 1 / Optimal Filters with Model 2 / Optimal Filters with Model 3 / Optimal Filters with Model 4 / Experimental Study

This work addresses this problem in the short-time Fourier transform (STFT) domain. We divide the general problem into five basic categories depending on the number of microphones being used and whether the interframe or interband correlation is considered. The first category deals with the single-channel problem where STFT coefficients at different frames and frequency bands are assumed to be independent. In this case, the noise reduction filter in each frequency band is basically a real gain. Since a gain does not improve the signal-to-noise ratio (SNR) for any given subband and frame, the noise reduction is basically achieved by liftering the subbands and frames that are less noisy while weighing down on those that are more noisy. The second category also concerns the single-channel problem. The difference is that now the interframe correlation is taken into account and a filter is applied in each subband instead of just a gain. The advantage of using the interframe correlation is that we can improve not only the long-time fullband SNR, but the frame-wise subband SNR as well. The third and fourth classes discuss the problem of multichannel noise reduction in the STFT domain with and without interframe correlation, respectively. In the last category, we consider the interband correlation in the design of the noise reduction filters. We illustrate the basic principle for the single-channel case as an example, while this concept can be generalized to other scenarios. In all categories, we propose different optimization cost functions from which we derive the optimal filters and we also define the performance measures that help analyzing them.

As speech processing devices like mobile phones, voice controlled devices, and hearing aids have increased in popularity, people expect them to work anywhere and at any time without user intervention. However, the presence of acoustical disturbances limits the use of these applications, degrades their performance, or causes the user difficulties in understanding the conversation or appreciating the device. A common way to reduce the effects of such disturbances is through the use of single-microphone noise reduction algorithms for speech enhancement. The field of single-microphone noise reduction for speech enhancement comprises a history of more than 30 years of research. In this survey, we wish to demonstrate the significant advances that have been made during the last decade in the field of discrete Fourier transform domain-based single-channel noise reduction for speech enhancement.Furthermore, our goal is to provide a concise description of a state-of-the-art speech enhancement system, and demonstrate the relative importance of the various building blocks of such a system. This allows the non-expert DSP practitioner to judge the relevance of each building block and to implement a close-to-optimal enhancement system for the particular application at hand. Table of Contents: Introduction / Single Channel Speech Enhancement: General Principles / DFT-Based Speech Enhancement Methods: Signal Model and Notation / Speech DFT Estimators / Speech Presence Probability Estimation / Noise PSD Estimation / Speech PSD Estimation / Performance Evaluation Methods / Simulation Experiments with Single-Channel Enhancement Systems / Future Directions

Digital measurement of the analog acoustical parameters of a music performance hall is difficult. The aim of such work is to create a digital acoustical derivation that is an accurate numerical representation of the complex analog characteristics of the hall. The present study describes the exponential sine sweep (ESS) measurement process in the derivation of an acoustical impulse response function (AIRF) of three music performance halls in Canada. It examines specific difficulties of the process, such as preventing the external effects of the measurement transducers from corrupting the derivation, and provides solutions, such as the use of filtering techniques in order to remove such unwanted effects. In addition, the book presents a novel method of numerical verification through mean-squared error (MSE) analysis in order to determine how accurately the derived AIRF represents the acoustical behavior of the actual hall.

This book introduces the theory, algorithms, and implementation techniques for efficient decoding in speech recognition mainly focusing on the Weighted Finite-State Transducer (WFST) approach. The decoding process for speech recognition is viewed as a search problem whose goal is to find a sequence of words that best matches an input speech signal. Since this process becomes computationally more expensive as the system vocabulary size increases, research has long been devoted to reducing the computational cost. Recently, the WFST approach has become an important state-of-the-art speech recognition technology, because it offers improved decoding speed with fewer recognition errors compared with conventional methods. However, it is not easy to understand all the algorithms used in this framework, and they are still in a black box for many people. In this book, we review the WFST approach and aim to provide comprehensive interpretations of WFST operations and decoding algorithms to help anyone who wants to understand, develop, and study WFST-based speech recognizers. We also mention recent advances in this framework and its applications to spoken language processing. Table of Contents: Introduction / Brief Overview of Speech Recognition / Introduction to Weighted Finite-State Transducers / Speech Recognition by Weighted Finite-State Transducers / Dynamic Decoders with On-the-fly WFST Operations / Summary and Perspective

This book addresses the problem of articulatory speech synthesis based on computed vocal tract geometries and the basic physics of sound production in it. Unlike conventional methods based on analysis/synthesis using the well-known source filter model, which assumes the independence of the excitation and filter, we treat the entire vocal apparatus as one mechanical system that produces sound by means of fluid dynamics. The vocal apparatus is represented as a three-dimensional time-varying mechanism and the sound propagation inside it is due to the non-planar propagation of acoustic waves through a viscous, compressible fluid described by the Navier-Stokes equations. We propose a combined minimum energy and minimum jerk criterion to compute the dynamics of the vocal tract during articulation. Theoretical error bounds and experimental results show that this method obtains a close match to the phonetic target positions while avoiding abrupt changes in the articulatory trajectory. The vocal folds are set into aerodynamic oscillation by the flow of air from the lungs. The modulated air stream then excites the moving vocal tract. This method shows strong evidence for source-filter interaction. Based on our results, we propose that the articulatory speech production model has the potential to synthesize speech and provide a compact parameterization of the speech signal that can be useful in a wide variety of speech signal processing problems. Table of Contents: Introduction / Literature Review / Estimation of Dynamic Articulatory Parameters / Construction of Articulatory Model Based on MRI Data / Vocal Fold Excitation Models / Experimental Results of Articulatory Synthesis / Conclusion

158 2. Wiener Filtering 159 3. Speech Enhancement by Short-Time Spectral Modification 3. 1 Short-Time Fourier Analysis and Synthesis 159 160 3. 2 Short-Time Wiener Filter 161 3. 3 Power Subtraction 3. 4 Magnitude Subtraction 162 3. 5 Parametric Wiener Filtering 163 164 3. 6 Review and Discussion Averaging Techniques for Envelope Estimation 169 4. 169 4. 1 Moving Average 170 4. 2 Single-Pole Recursion 170 4. 3 Two-Sided Single-Pole Recursion 4. 4 Nonlinear Data Processing 171 5. Example Implementation 172 5. 1 Subband Filter Bank Architecture 172 173 5. 2 A-Posteriori-SNR Voice Activity Detector 5. 3 Example 175 6. Conclusion 175 Part IV Microphone Arrays 10 Superdirectional Microphone Arrays 181 Gary W. Elko 1. Introduction 181 2. Differential Microphone Arrays 182 3. Array Directional Gain 192 4. Optimal Arrays for Spherically Isotropic Fields 193 4. 1 Maximum Gain for Omnidirectional Microphones 193 4. 2 Maximum Directivity Index for Differential Microphones 195 4. 3 Maximimum Front-to-Back Ratio 197 4. 4 Minimum Peak Directional Response 200 4. 5 Beamwidth 201 5. Design Examples 201 5. 1 First-Order Designs 202 5. 2 Second-Order Designs 207 5. 3 Third-Order Designs 216 5. 4 Higher-Order designs 221 6. Optimal Arrays for Cylindrically Isotropic Fields 222 6. 1 Maximum Gain for Omnidirectional Microphones 222 6. 2 Optimal Weights for Maximum Directional Gain 224 6. 3 Solution for Optimal Weights for Maximum Front-to-Back Ratio for Cylindrical Noise 225 7. Sensitivity to Microphone Mismatch and Noise 230 8.

Many new DCT-like transforms have been proposed since the first edition of this book. For example, the integer DCT that yields integer transform coefficients, the directional DCT to take advantage of several directions of the image and the steerable DCT. The advent of higher dimensional frames such as UHDTV and 4K-TV demand for small and large transform blocks to encode small or large similar areas respectively in an efficient way. Therefore, a new updated book on DCT, adapted to the modern days, considering the new advances in this area and targeted for students, researchers and the industry is a necessity.