## Optimal Time-Domain Noise Reduction Filters: A Theoretical StudyAdditive noise is ubiquitous in acoustics environments and can affect the intelligibility and quality of speech signals. Therefore, a so-called noise reduction algorithm is required to mitigate the effect of the noise that is picked up by the microphones. This work proposes a general framework in the time domain for the single and multiple microphone cases, from which it is very convenient to derive, study, and analyze all kind of optimal noise reduction filters. Not only that all known algorithms can be deduced from this approach, shedding more light on how they function, but new ones can be discovered as well. |

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### Contents

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3 SingleChannel Noise Reduction with a Rectangular Filtering Matrix | 23 |

4 Multichannel Noise Reduction with a Filtering Vector | 42 |

### Other editions - View all

Optimal Time-Domain Noise Reduction Filters: A Theoretical Study Jacob Benesty,Jingdong Chen No preview available - 2011 |

### Common terms and phrases

algorithms beamformers Benesty Chap chapter Chen constraint correlation matrix cross-correlation deduce define the error derived desired signal vector desired speech signal diagonal matrix eigenvalue eigenvector error signal vector estimate filtered desired signal hLCMV Huang identity filtering matrix identity matrix IEEE IEEE Trans input SNR interference signal iSNR joint diagonalization Lagrange multiplier LCMV length NL Linear Filtering linear transformation maximum SNR filtering Microphone Array microphone signal minimizing MSE criterion MVDR filtering matrix noise reduction factor Noise Reduction Filters noise signal optimal filtering matrices optimal filtering vectors orthogonal oSNR Hmax oSNR HMVDR oSNR(h output SNR particular filtering performance measures rectangular filtering matrix residual noise scaling factor signal model Signal Process speech distortion index speech enhancement Speech Processing speech reduction factor Speech Signal Process square matrix Time-Domain Noise Reduction TxxM uncorrelated variance vector of length vector y(k Wiener filtering matrix xfd(k xi(k xM(k