Estimation of allpass transfer functions by introducing sparsity constraints to particle swarm optimization

An algorithm to estimate allpass transfer functions by assuming sparsity over the input signals is proposed in this paper. As a tractable measure of sparsity, the l₁ norm of input signal is minimized and the set of allpass coefficients which realizes the l₁ norm minimization is obtained. It is observed that the estimation of allpass systems with sparse inputs is a nonconvex problem and hence a nonconvex optimization method-the particle swarm optimization (PSO) is used. With PSO, a large number of uniformly chosen points in a d-dimensional problem space are guided towards an optimum solution with respect to the l₁ norm of input signal. Experimental results show that PSO is successful in estimating allpass transfer functions. Application of allpass filter estimation to speech processing is also studied and results which portray the effectiveness of the proposed method are reported.