Audio Signals Noise Removal Real Time System Sorin Zoican, Ph.D. POLITEHNICA University of Bucharest sorin@elcom.pub.ro Abstract: This paper presents a real time implementation of a noise removal system for audio signals. This system is based on the wavelet approach with level dependant threshold that provides a useful method for noise elimination in the signals. Experimental results show that this method removes noise significantly and the system operates in real time. Keywords: noise, wavelet transform, inverse wavelet transform, coefficient, finite impulse response filter (FIR), digital signal processor (DSP), real time. I. INTRODUCTION For audio signals, noise may be introduced by recording medium or transmission medium. Over the last years, there has been a very great interest for noise removal in such signals. The approach used in a noise removal system should have two main characteristics: eliminates most of the noise components and works in real time. The wavelet shrinkage method represents a noise removal procedure by shrinking the wavelet coefficients below a given threshold in the wavelet domain. Originally, it was proposed the use of a universal threshold uniformly throughout the entire wavelet decomposition tree. Then the use of the wavelet tree was found to be more efficient [1]. Some methods of selecting thresholds that are adaptive to different spatial characteristics have been proposed and investigated [2]. In this paper a level dependant threshold is involved. In such approach, the threshold is computed for each level in wavelet decomposition tree. The paper is organized in several sections. Section II presents the noise adaptive algorithm, including the wavelet threshold. The real time system, implemented with a digital signal processor (DSP) – ADSP2181 from Analog Devices – is illustrated in section III. Experimental results and the performance evaluation are given in section IV. The conclusion is presented in section V. II. THE NOISE REMOVAL ALGORITHM In the wavelet analysis, we deal with coefficients approximations (CA) and coefficients details (CD). The approximations are the high-scale, low-frequency components of the signal. The details are the low-scale, high-frequency components. For the discrete wavelet transform, the decomposition process is shown in figure 1. In this figure, the symbol ↓2 represents down sampling by 2. The principle under which the wavelet de-noising approach operates relies on the fact that for many real life signals, a limited number of wavelet coefficients in the lower bands are sufficient to reconstruct a good estimate of the original signal. Usually these coefficients are relatively large compared to other coefficients or to any other signal (especially noise) that has its energy spread over a large number of coefficients. Therefore, by shrinking coefficients smaller than a specific value, called threshold, we can nearly eliminate noise while preserving the important information of the original signal The proposed noise removal algorithm is summarized as follows: a) Compute the discrete wavelet transform for noisy signal. b) Shrink some detail wavelet coefficients, accordingly with a given threshold. c) Compute the inverse discrete wavelet transform. The whole process is shown in the figures 1, 2 and 3. The shrinkage function functions used is defined as the relation (1): T x T x x T x f T < ≥ = | | , 0 | | , ) , ( (1) In this paper, level dependent thresholds [2] define by relation (2), is used: ) ln( 2 k k k N T σ = (2) where k N is the number of the samples in the level k and 6745 . 0 ) ( k k C Median = σ (3) in which ) ( k C Median represents the median value of the coefficients on the level k. The shrinkage process is illustrated in the figure 2. After the processing of the wavelet coefficients, the processed components can be assembled back into the enhanced 978-1-4244-6363-3/10/$26.00 c 2010 IEEE 25