Circuits and Systems, 2013, 4, 459-465 Published Online November 2013 (http://www.scirp.org/journal/cs) http://dx.doi.org/10.4236/cs.2013.47060 Open Access CS A Robust Denoising Algorithm for Sounds of Musical Instruments Using Wavelet Packet Transform Raghavendra Sharma, Vuppuluri Prem Pyara Department of Electrical Engineering, Dayalbagh Educational Institute, Agra, India Email: raghsharma2000@yahoo.com Received September 17, 2013; revised October 17, 2013; accepted October 24, 2013 Copyright © 2013 Raghavendra Sharma, Vuppuluri Prem Pyara. This is an open access article distributed under the Creative Com- mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT In this paper, a robust DWPT based adaptive bock algorithm with modified threshold for denoising the sounds of musi- cal instruments shehnai, dafli and flute is proposed. The signal is first segmented into multiple blocks depending upon the minimum mean square criteria in each block, and then thresholding methods are used for each block. All the blocks obtained after denoising the individual block are concatenated to get the final denoised signal. The discrete wavelet packet transform provides more coefficients than the conventional discrete wavelet transform (DWT), representing ad- ditional subtle detail of the signal but decision of optimal decomposition level is very important. When the sound signal corrupted with additive white Gaussian noise is passed through this algorithm, the obtained peak signal to noise ratio (PSNR) depends upon the level of decomposition along with shape of the wavelet. Hence, the optimal wavelet and level of decomposition may be different for each signal. The obtained denoised signal with this algorithm is close to the original signal. Keywords: DWPT; Adaptive Block Denoising; Peak Signal to Noise Ratio; Wavelet Thresholding 1. Introduction In the field of denoising the sounds of musical instru- ments, time frequency based transforms play an impor- tant role. They allow us to work with a sound signal from both time and frequency perspectives simultaneously. Such transforms have traditionally been useful in study- ing the nature of the sound signal, noise, and in facilitat- ing the application of aesthetically interesting and novel modification to specific sound signals [1]. We are inter- ested in a transform that is useful in working with musi- cal instrument sound signals, and we look at the applica- tion of the discrete wavelet packet transform (DWPT) to remove the additive white Gaussian noise. There are several reasons for choosing the DWPT, it is inherently multi-resolution, making it more suited to human psyc- hoacoustics than fixed resolution transforms as short time Fourier transform (STFT) [2]. It is easily reconfigured to allocate time frequency resolution in different ways through various basis selection approaches. Furthermore, efficient discrete time algorithms are available, and the transform basis function is inherently time localized without the introduction of a separate window function. Signals may be transformed, modified and re-synthesized using DWPT without affecting the quality of the signal [3]. Noise has been a major problem for all signal proc- essing applications. An unwanted signal gets superim- posed over clean undisturbed signal. Noise exists in high frequency, but the sound signal is primarily low fre- quency. Since the wavelet transform decomposes the sig- nal into approximation (low frequency) and detail (high frequency) coefficients [4,5], much of the noise is con- centrated in detail coefficients. This suggests a method to denoise the signal, simply reducing the size of the detail coefficients before using them to reconstruct the signal, which is called thresholding or shrinkage rule [6]. We cannot eliminate the detail coefficients entirely, because they contain some important information of the signal. Various kinds of thresholding have been proposed in literature [7], but the choice depends upon the application at hand. The two important types of thresholing, hard and soft have been used to denoise the signal. In hard thresh- olding the wavelet coefficients below the given threshold are set to zero, but in soft thresholding the wavelet coef- ficients are reduced by a quantity equal to the threshold