A Perspective on Single-channel Frequency-domain Speech Enhancement
Morgan & Claypool Publishers, 2011 - Technology & Engineering - 101 pages
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
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acoustic signal processing Chapter clean speech components constraint covariance matrix deduce define the narrowband desired signal domain error signal filter with Model forgetting factors frequency frequency-bin frequency-domain fullband input SNR fullband noise reduction fullband output SNR fullband performance fullband speech distortion fullband speech reduction hH(k hMVDR hMVDR(k hW(k iMVDR interframe correlation iSNR iSNR(fc iSNR(k Jacob Benesty kmax(k Lagrange multiplier m)ii maximum SNR filter minimizing MVDR filter narrowband and fullband narrowband input SNR narrowband MSE narrowband output SNR narrowband SNR narrowband speech distortion NMSE noise reduction factor noncircularity optimal filters oSNR performance measures Proof Property pv(k px(k residual interference residual interference-plus-noise residual noise result scaling factor SCNR short-time Fourier transform signal is distorted spectral amplitude speech distortion index speech reduction factor speech signal STFT tradeoff filter tradeoff gain uncorrelated upper bounded vector Vk,m Vm(k Wiener and MVDR Wiener filter window Xld(k yv(k yx(k yy(k