New PDF release: Sparse Adaptive Filters for Echo Cancellation (Synthesis

By Jacob Benesty, Constantin Paleologu, Silviu Ciochina, B.H. Juang

ISBN-10: 1598293060

ISBN-13: 9781598293067

Adaptive filters with various coefficients are typically enthusiastic about either community and acoustic echo cancellation. hence, you will need to increase the convergence cost and monitoring of the traditional algorithms used for those purposes. this is completed through exploiting the sparseness personality of the echo paths. id of sparse impulse responses used to be addressed customarily within the final decade with the advance of the so-called ``proportionate''-type algorithms. The objective of this booklet is to provide crucial sparse adaptive filters constructed for echo cancellation. in addition to a finished evaluation of the elemental proportionate-type algorithms, we additionally current a few of the most up-to-date advancements within the box and suggest a few new ideas for additional functionality development, e.g., variable step-size types and novel proportionate-type affine projection algorithms. An experimental learn is usually supplied with a view to evaluate many sparse adaptive filters in numerous echo cancellation eventualities. desk of Contents: advent / Sparseness Measures / functionality Measures / Wiener and uncomplicated Adaptive Filters / easy Proportionate-Type NLMS Adaptive Filters / The Exponentiated Gradient Algorithms / The Mu-Law PNLMS and different PNLMS-Type Algorithms / Variable Step-Size PNLMS Algorithms / Proportionate Affine Projection Algorithms / Experimental learn

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Furthermore, the active regions of the echo path do not have to be detected explicitly. In the PNLMS, the diagonal elements of G(n − 1) are calculated as (18) γmin (n − 1) = max δp , hˆ 0 (n − 1) , . . 01, = 5/L. The term γmin (n − 1) prevents hˆ l (n − 1) from stalling when it is much smaller than the magnitude of 40 5. 1: The proportionate NLMS (PNLMS) algorithm. Initialization: Parameters: Error: Update: hˆ l (0) = 0, l = 0, 1, . . 01 = 5/L 0<α<2 δPNLMS = cst · σx2 /L ˆ − 1) e(n) = d(n) − x T (n)h(n γmin (n − 1) = max δp , hˆ 0 (n − 1) , .

On the other hand, when the algorithm starts to converge to the true solution, σe (n) ≈ σw and μNPVSS (n) ≈ 0. This is exactly what we desire to have both good convergence and low misadjustment. As we can notice, this approach was derived with almost no assumptions compared to all other algorithms belonging to the same family. 3 summarizes a practical version of the NPVSS-NLMS algorithm. 4. 3: The non-parametric VSS-NLMS (NPVSS-NLMS) algorithm. Initialization: Parameters: Error: Update: ˆ h(0) =0 2 σˆ e (0) = 0 1 , exponential window with K ≥ 2 KL σw2 , noise variance known or estimated δ = cst · σx2 , regularization > 0, very small number to avoid division by zero T e(n) = d(n) − hˆ (n − 1)x(n) λ=1− σˆ e2 (n) = λσˆ e2 (n − 1) + (1 − λ)e2 (n) σw −1 ς (n) = δ + xT (n)x(n) 1− + σˆ e (n) ς (n) if σˆ e (n) ≥ σw μNPVSS (n) = 0 otherwise ˆh(n) = h(n ˆ − 1) + μNPVSS (n)x(n)e(n) Similar, at first glance, with the NPVSS-NLMS, a so-called set membership NLMS (SMNLMS) algorithm was proposed earlier in (28).

Another idea with a variable parameter in the IPNLMS, similar to the one just presented, can be found in (45). 2 THE IPNLMS WITH THE 0 NORM It can be noticed that the regular IPNLMS algorithm uses the 1 norm to exploit the sparsity of the impulse response that we need to identify. A better measure can be the 0 norm since it is a natural mathematical measure of sparseness (16), (52). However, the function f (hl ), associated with the 0 norm (see Chapter 2), is not continuous, and because that many elements of the vector h can be very small but not exactly zero, it is better to approximate it by a smooth and continuous function.

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Sparse Adaptive Filters for Echo Cancellation (Synthesis Lectures on Speech and Audio Processing) by Jacob Benesty, Constantin Paleologu, Silviu Ciochina, B.H. Juang


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