By Steven L. Gay, Jacob Benesty
158 2. Wiener Filtering 159 three. Speech Enhancement by means 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 energy Subtraction three. four value Subtraction 162 three. five Parametric Wiener Filtering 163 164 three. 6 evaluation and dialogue Averaging innovations for Envelope Estimation 169 four. 169 four. 1 relocating normal a hundred and seventy four. 2 Single-Pole Recursion one hundred seventy four. three Two-Sided Single-Pole Recursion four. four Nonlinear facts Processing 171 five. instance Implementation 172 five. 1 Subband clear out financial institution structure 172 173 five. 2 A-Posteriori-SNR Voice job Detector five. three instance one 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 top 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 optimum Directional achieve 224 6. three resolution 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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Additional resources for Acoustic Signal Processing for Telecommunication
100 150 200 250 samples (in hundreds) 300 350 400 Comparison of FAP for different orders of projection, N, with speech as excitation. 3 shows a comparison of the convergence of NLMS, FTF (Fast Transversal Filter, an FRLS technique), and FAP coefficient error magnitudes. The excitation signal was speech sampled at 8 kHz, the echo path of length, L = 1000, was fixed and the white gaussian additive noise, Yn, was 30 dB down from the echo. Soft initialization was used for both algorithms. o and Eb,O were set to 8 = 200-;' and N was 50.
En is the a priori error (or simply, the "error") or the residual echo. 7) where hn is chosen so as to decrease the value of J (h). 11) h=hn-l where the constant of proportionality, fL is called the stepsize. 1) in the last step. 12) is simply ignored. 14) The average coefficient vector convergence is easily derived  by first restoring the expectations. 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.
Acoustic Signal Processing for Telecommunication © Springer Science+Business Media New York 2000 24 Acoustic Signal Processing advantageous because usually N is much smaller than L. FAP uses a sliding windowed FRLS  to assist in a recursive calculation of the solution. Since sliding windowed FRLS algorithms easily incorporate regularization of the covariance matrix inverse, FAP is regularized as well, making it robust to measurement noise. The complexity of FAP is roughly 2L + 20N multiplications per sample period.