I.J. Image, Graphics and Signal Processing, 2013, 6, 1-8 Published Online May 2013 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijigsp.2013.06.01 Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 6, 1-8 Genetic Algorithm For Designing QMF Banks and Its Application In Speech Compression Using Wavelets Noureddine Aloui , Ben Nasr Mohamed , Adnane Cherif Innov‟ Com Group, Signal Processing Laboratory, Sciences Faculty of Tunis, University of Tunis El-Manar, TUNIS, 1060, TUNISIA. aloui.noureddine@gmail.com, bennasr.mohamed@gmail.com, adnane.cher@fst.rnu.tn Abstract— In this paper, real-coded genetic algorithm (GA) is used for designing two-channel quadrature mirror filter (QMF) banks based on the Kaiser Window. The shape of the Kaiser window and the cutoff frequency of the prototype filter are optimized using a simple GA. The optimized QMF banks are exploited as mother wavelets for speech compression based on discret wavelet transform (DWT). The simulation results show the efficiency of the GA for designing QMF banks using adjustable windows length and especially for optimizing wavelet filters used in speech compression based on wavelets. In addition, a comparative of performance of the developed wavelets filters using GA and others known wavelets is made in term of objective criteria (CR, SNR, PSNR, and NRMSE). The simulation results show that the optimized wavelets filters outperform others wavelets already exist used for speech compression. Index Terms— Quadrature mirror filter, Real-coded Genetic Algorithm, Speech compression, discret wavelet transform, window techniques I. I NTRODUCTION Quadrature Mirror Filter (QMF) banks are most commonly used in many signal processing applications such as: sub-band coding of speech and image signals [10][11][12], audio, image or video processing and its compression [13][14][15], transmultiplexer [16], design of wavelet bases and communication systems [17] and others applications. Therefore, several techniques have been presented for designing the QMF banks based on linear and non-linear phase objective function. In [2], author has introduced the theory of two-band linear phase QMF banks and design a family of filters using non-linear optimization based Hooke and Jeaves optimization algorithm [19] and a Hanning window [2]. A linear optimization method has introduced in [19] for designing M-band QMF banks, this method consists in iteratively adjusting the pass-band to minimize the reconstruction error. Thereafter, several new iterative algorithms [20] [21] [22] [22] [23] [24] [25] have been developed using window technique to optimize QMF banks design. However, the used window functions can be classified into two categories: the first category is fixed length window such as Hamming, Hanning and Rectangular window; the main lobe width is controlled only by window length. The second category is adjustable length window; the main lobe is controlled by the window length and one or more additional parameters such as the shape window used for controlling the spectral characteristics [1]. In the above context, in this work a real-coded GA is exploited for designing a QMF banks based on adjustable windows length. The paper is divided into four sections, as follows. Section 1, discusses the analysis and synthesis using two-channel QMF banks. Section 2, presents the proposed methodology for designing QMF banks using real-coded GA. Section 3, attempted to explain the principle of speech compression using DWT. Finally, comparative study between the optimized wavelet filters using GA and the others known wavelets is carried out in section four. II. TWO-CHANNEL QMF BANKS The basic structure of two-channel QMF bank is illustrated in figure 1. The analysis step consists in split the input signal () x n into two frequency bands by a low-pass analysis filter 0 () H z and a high-pass analysis filter 1 () H z . Then, the obtained subbands are down sampled by factor of two. In the synthesis step, each subband is up-sampled by factor of two, and then passing through low-pass synthesis filter 0 () G z and high-pass synthesis filter 1 () G z . Finally, the obtained sub-bands are recombined to reconstruct signal () y n . Figure 1. Two-channel Quadrature mirror filter banks. x(n) y(n) Analysis Synthesis H0(z) ↓2 processing + G0(z) ↑2 H1(z) ↓2 G1(z) ↑2