# Acoustic Signal Processing for Telecommunication - download pdf or read online

By Steven L. Gay, Jacob Benesty

158 2. Wiener Filtering 159 three. Speech Enhancement by way of Short-Time Spectral amendment three. 1 Short-Time Fourier research and Synthesis 159 a hundred and sixty three. 2 Short-Time Wiener clear out 161 three. three strength Subtraction three. four importance Subtraction 162 three. five Parametric Wiener Filtering 163 164 three. 6 evaluate and dialogue Averaging concepts for Envelope Estimation 169 four. 169 four. 1 relocating commonplace a hundred and seventy four. 2 Single-Pole Recursion a hundred and seventy four. three Two-Sided Single-Pole Recursion four. four Nonlinear info Processing 171 five. instance Implementation 172 five. 1 Subband filter out financial institution structure 172 173 five. 2 A-Posteriori-SNR Voice job Detector five. three instance a hundred seventy five 6. end a hundred seventy five half IV Microphone Arrays 10 Superdirectional Microphone Arrays 181 Gary W. Elko 1. creation 181 2. Differential Microphone Arrays 182 three. Array Directional achieve 192 four. optimum Arrays for Spherically Isotropic Fields 193 four. 1 greatest achieve for Omnidirectional Microphones 193 four. 2 greatest Directivity Index for Differential Microphones 195 four. three Maximimum Front-to-Back Ratio 197 four. four minimal height Directional reaction 2 hundred four. five Beamwidth 201 five. layout Examples 201 five. 1 First-Order Designs 202 five. 2 Second-Order Designs 207 five. three Third-Order Designs 216 five. four Higher-Order designs 221 6. optimum Arrays for Cylindrically Isotropic Fields 222 6. 1 greatest achieve for Omnidirectional Microphones 222 6. 2 optimum Weights for max Directional achieve 224 6. three answer for optimum Weights for optimum Front-to-Back Ratio for Cylindrical Noise 225 7. Sensitivity to Microphone Mismatch and Noise 230 8.

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**Extra resources for Acoustic Signal Processing for Telecommunication**

**Example text**

While this is a perfectly valid interpretation, another one that lends itself to generalization (and also improved performance) is NLMS as an affine projection. This is discussed in Chapter 2. 23) An Introduction to Acoustic Echo and Noise Control 13 where for the moment we leave undefined the exact bounds on the samples comprising the matrices and vectors except to say that, at least after the first N sample periods, N, the length of the error vector is greater than, L, the length of the filter.

22) 0 where there are N ones and L - N zeros in the diagonal matrix. L < 1. 15). 17), where now Q = Qn and f = Pnhep. 23)]. 23) gives us an intuitive feel for the convergence of h n to h ep . L = 1. We see that as N increases from 1 toward L, the contribution to h n from hn-l decreases because the nullity of Qn is increasing, while the contribution from hep increases because the rank of P n is increasing. In principle, when N = L, h n should converge to hep in one step, since Qn has a rank of zero and P n a rank of L.

13) in (1. 15) Let Axx,i represent the eigenvalues of Rxx. 16) So, for h n to converge to hopt> we must have, for i = 1, ... 17) Since Rxx is positive definite, all its eigenvalues are positive. So, the maximum eigenvalue of Rxx is less than the sum of its eigenvalues. The sum of the eigenvalues is equal to the trace which in this case is just L times the variance of n , Therefore, if we choose fL such that x a-;. 18) then the convergence of the average of h n is guaranteed. J, is determined, modes with smaller eigenvalues will converge slower than those with large ones.