Study of Signal Denoising using Kaiser Window and Butterworth Filter

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1 International Journal of Electronics and Computer Science Engineering 087 Available Online at ISSN Study of Signal Denoising using Kaiser Window and Butterworth Filter Richa Gupta, Onkar Chand 2 Department of Electronics and Communication Engineering I.E.T Bhaddal (PTU) - richaguptta@yahoo.co.in,bkonkar.chd@gmail.com Abstract: A signal in the communication system is the information containing part which is to be process, but during the processing of the signal some noise is added in the signal and signal becomes noisy. This is now mandatory to eliminate this noise from the signal to get information from the signal. In this paper, a wavelet filter based on Butterworth IIR filter and Kaiser Window FIR filter is designed for the signal analysis. Butterworth low pass IIR filter has limited application in signal denoising. It has maximally flat response in the pass band and, therefore, the filter has distorted output. It makes Butterworth filter little applicable in communication systems and other signal analysis technique. The newly designed matched wavelet filter presents a new concept for better signal analysis and disturbance detection in the communication systems. The limitation of Butterworth low pass filter in signal denoising and other applications can be eliminated by using this matched wavelet filter. We have improved performance in signal filtering by using Kaiser Wavelet filter. This Wavelet filter finds applications in signal analysis, communication system and image compression with a lot of other fields. Keywords: Wavelets, FIR, Butterworth Filter, Kaiser Window, Chebyshev Filter. I. DEFINATION OF WAVELET Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing the situations where the signal contains discontinuities and sharp spikes. Wavelets were developed independently in the field of the quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, and earthquake prediction. The fundamental idea behind wavelets is to analyze according to scale. Indeed, some researchers in the wavelet field feel that, by using wavelets, one is adopting a whole new mindset or perspective in processing data. Approximation using superposition of functions has existed since the early 800's, when Joseph Fourier discovered that he could superpose sines and cosines to represent other functions. However, in wavelet certain mathematical requirements and are used in representing data or other functions. analysis, the scale that we use to look at data plays a special role. II REVIEW WORK I Statistically Matched Wavelet Design: The paper [4] presents the design of statistically matched wavelet filter banks that have been extensively studied where it has been formulated as a constrained optimization problem. To assess the coding gain performance of matched filter banks designed according to Vis-&Vis that of the KLT, it is need to extend the parametric analysis. Let Rxx denote the covariance matrix of a process and let the vector, h, of size 2M, consists of the filter coefficients. The matched wavelet that maximizes the energy compaction can be formulated in terms of the objective function J=hTRXXh +λo[-hth]+µ[htch]+µm[htcmh]..()

2 IJECSE,Volume,Number 3 Richa Gupta et al. II. Constructing Wavelets from Desired Signal Functions- In the paper [5], author presents the most applications of orthonormal multiresolution analyses (OMRA) use either Daubechies, Meyer s, or Lemarie s wavelets. However, it would be best if the wavelet matched the signal of interest. The paper [5],presents a technique for generating an OMRA with a wavelet that is matched in the least squares sense to a signal of interest by first developing a method for constructing the scaling function from the wavelet and second, giving the conditions on the wavelet that guarantee an OMRA [6]. III Distributed Signal Processing via Chebyshev Polynomial Approximation- Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of the graph multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be applied to distributed processing tasks such as smoothing, denoising, inverse filtering, and semi-supervised classification, and show that the communication requirements of the method scale gracefully with the size of the network. IV Speech Denoising Using Different Types of Filters- Speech Recognition is a broader solution which refers to a technology that can recognize a speech without being targeted at single speaker such call system can recognize arbitrary voice. The fundamental purpose of speech is communication, i.e., the transmission of messages. The problem in speech recognition is the speech pattern variability. The most challenging sources of variations in speech are speaker characteristics including accent, coarticulation and background noise. The filter bank in the front-end of a speech recognition system mimics the function of the basilar membrane. It is believed that closer the band subdivision to human perception better is the recognition results. Filter constructed from estimation of clean speech and noise for speech enhancement in speech recognition systems. In my work, I am using a filter on the frequency spectrum of an input voice, firstly that will record the voice and after that the same will played on simulation and it will give the frequency spectrum. Finally, this spectrum will be filtered to remove noise. III PROPOSED APPROACH From the above literature survey, we conclude that wavelet filters are to design as per the requirement of signal denoising. IIR window technique property of wavelet is the key point in the development of Wavelet Filters. A matched wavelet filter may also be designed by using FIR (Finite Impulse Response) Filters. But, a few of the researchers have focused on to design of matched wavelet filters using IIR filters. There are less number of approaches available for designing of IIR (Infinite Impulse Response) Filters, also known as all pass filters, than FIR Filters. A potential drawback is the division required in the computation of the coefficients, which are slow and difficult to implement, e.g., with digital signal processors. In this report, focus is on designing matched wavelet through IIR Filter coefficients and FIR Filter coefficients both. I. Introduction to IIR Filters- Filters are the electronic circuits which have the functionality to remove the unwanted frequency components from the signal.in the field of the digital signal processing, filters have the numerous applications. In signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range. Filters have functions of the signal separation and signal restoration [8]. The signal separation is done when signal is affected by the interference, noise or by other noise factors. For example, imagine a device for measuring the electrical activity of a baby's heart while still in the womb. The raw signal will likely be corrupted by the breathing and heartbeat of the mother. A filter might be used to separate these signals so that they can be individually analyzed. Signal restoration is used when a signal has been distorted in some way. For example, an audio recording made with poor equipment may be filtered to

3 Study of Signal Denoising using Kaiser Window and Butterworth Filter 089 better represent the sound as it actually occurred. Another example is the deblurring of an image acquired with an improperly focused lens, or a shaky camera. A. Introduction to Butterworth filter and Calculation of order and coefficients- The Butterworth filter is one type of signal processing filter design. It is designed to have a frequency response which is as flat as mathematically possible in the pass band. Another name for it is flat maximally magnitude filter. The Butterworth type filter was first described by the British engineer Stephen Butterworth. Butterworth solved the equations for two and four pole filters and showed how the latter could be cascaded when separated by vacuum tube amplifiers. This made possible the construction of higher order filters in spite of inductor losses. In 930, low loss core materials such as molypermalloy had not been discovered and air core audio inductors were rather lossy. Butterworth discovered that it was possible to adjust the component values of the filter to compensate for the winding resistance of the inductors. The frequency response of the Butterworth filter is maximally flat (has no ripples) in the pass band, and rolls off towards zero in the stop band. When viewed on a logarithmic Bode plot, the response slopes off linearly towards negative infinity. For a first-order filter, the response rolls off at 6 db per octave ( 20 db per decade) (all firstorder low pass filters have the same normalized frequency response). For a second-order low pass filter, the response ultimately decreases at 2 db per octave, a third-order at 8 db, and so on. Figure.: Frequency Response of the Butterworth filter. Butterworth filters have a monotonically changing magnitude function with ω, unlike other filter types that have non-monotonic ripple in the pass band and/or the stop band. Compared with a Chebyshev Type I/Type II filter or an elliptic filter, the Butterworth filter has a slower roll-off, and thus will require a higher order to implement a particular stop band specification. However, Butterworth filters have a more linear phase response in the pass band than the Chebyshev Type I/Type II and elliptic filters. The squared response of the Butterworth filter is given as the function of the cut-off frequency. H a (j Ω ) 2 = 2n...(2) Ω The maximum pass band edge attenuation is H a (j Ω p ) = 2n (3) Ωp + (Ω p /Ω c ) 2n =ε 2.(4) So the order of the filter is calculated from the pass edge frequency

4 IJECSE,Volume,Number 3 Richa Gupta et al. logε n= (5) log Ωp log Ωc The minimum stop band edge attenuation is calculated as; H a (j Ω s ) 2 = 2n (6) Ωs + The transfer function H a (j Ω s) of the Butterworth filter is calculated from the order of the filter. H * a (j Ω ha )=[ (t) e -jωt dt] (7) 0 From the above given expression the filter order and the coefficients are calculated. II Digital FIR Filter- Figure2: Region of convergence for the transfer function of the filter. FIR filters are widely used due to the powerful design algorithms that exist for them, their inherent stability when implement in non-recursive form, the ease with which one can attain linear phase, their simple extensibility to multirate cases, and the ample hardware support that exists for them among other reasons. In order to determine a suitable filter order, it is necessary to specify the amount of passband ripple and stopband attenuation that will be tolerated. It is also necessary to specify the width of the transition region around the ideal cutoff frequency. The latter is done by setting the passband edge frequency and the stopband edge frequency the difference between the two determines the transition width. Next section provide the brief introduction of Kaiser window used in analysis. B Kaiser Window- To obtain a Kaiser window that designs an FIR filter with side lobe attenuation of α db, Kaiser window parameter β that affects the side lobe attenuation of the Fourier transform of the window is given by β = 0.02(α 8.7), α > (α 2) (α 2),2 α 50 (8) 0, α < 2 Where α =-20 log 0 δ is the stop band attenuation expressed in decibels. Increasing β widens the main lobe and decreases the amplitude of the side lobes (i.e., increases the attenuation). Filter order for FIR filter is given by

5 Study of Signal Denoising using Kaiser Window and Butterworth Filter 09 N=(α-8/2.285 w)+.(9) Here N is the filter order and w is the width of the smallest transition region. IV CONCLUSION Now-a-days, noises are common in communication channels and the recovery of the transmitted signals from the communication path without any noise is considered as one of the difficult tasks. This is accomplished by the denoising techniques that remove noises from a digital signal. Various denoising technique have been proposed till date for the removal of noises from the digital audio signals. Yet, the effectiveness of those techniques remains an issue. In this paper I have included the newly designed matched wavelet filter concept for better signal analysis and disturbance detection in the communication systems. V REFERENCE [] Alyson K. Fletcher, Vivek K Goyal and Kannan Ramchandran, "Iterative Projective Wavelet Methods for Denoising", Proc. Wavelets X, part of the 2003 SPIE Int. Symp. On Optical Science & Technology, Vol. 5207, pp: 9-5, San Diego, CA August. [2] Claudia Schremmer, Thomas Haenselmann and Florian Bomers, 200. "A Wavelet Based Audio Denoiser", In Proc. IEEE International Conference on Multimedia and Expo (ICME'200), pp: [3] S.Pooranchandra, N.Kumaravel, A novel method for Elimination of power line frequency in ECG signal using hyper shrinkage function, Digital Signal Processing, Volume8, Issue 2, March 2008, pp [4] Alireza K Ziarani, Adaibert Konrad, Non linear Adaptive method of elimination of power line interference in EC signals, IEEE Transactions on Biomedical Engg, Vol.49 No.6, June 2002, pp [5] Santpal Singh Dhillon, Saswat Chakrabarti, Power Line Interference removal From Electrocardiogram Using Simplified Lattice Based Adaptive IIR Notch Filter, Proceedings of the 23rd Annual EMBS International conference, October 25-28, Istanbul, Turkey, 200 pp [6] Mahesh S.Chavan, R.A.Aggarwala, M.D.Uplane, Interference reduction in ECG using digital FIR filters based on Rectangular window, WSEAS Transactions on Signal Processing, Issue 5, Volume 4, May 2008, pp [7] Joseph O. Chapa and Raghuveer M. Rao, Algorithms for Designing Wavelets to matched a specified signal, IEEE Transactions on Signal Processing, vol. 48, no.2, Dec [8] Emin Anarim, et.al, Design Issues For Matcheded Wavelets, Bogazici University,Turkey, June 994. [9] Major Joseph 0. Chapa, Constructing Wavelets from Desired Signal Functions Center for Imaging Science, Rochester Institute of Technology, Rochester, NY 4623, USA. [0] S.G. Mallat, A Theory for Multiresolution Signal Decomposition: The. Wavelet Tkansform, IEEE Transactions on Pattern Analysis and Machine Intelligence, v., no. 7, July 989. [] C. K. Chui, An Introduction to Wavelets, Wavelet Analysis and Its Application, Vol I, Academic Press, Inc., 992. [2] L.R.Rabiner and B.Gold, Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall 975. [3] Insight into Wavelets, by K.P. Soman & K.I. Ramachandran. [4] L.R.Rabiner and B.Gold, Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 975. [5] Enqing Dong and Xiaoxiang Pu, "Speech denoising based on perceptual weighting filter," Proceedings of 9th IEE International Conference on Signal Processing, pp: , October 26-29, Beijing.