design of adaptive noise canceller using lms algorithm - ijater

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International Journal of Advanced Technology & Engineering Research (IJATER)www.ijater.comAdaptive Filter :Concept of adaptive filterrealize the adaptive noise cancellation, we use twoinputs and an adaptive filter. One input is the signalcorrupted by noise (Primary Input, which can beexpressed as s(n) x1(n)). The other input containsnoise related in some way to that in the main inputbut does not contain anything related to the signal(Noise Reference Input, expressed as x(n)). The noisereference input pass through the adaptive filter andoutput y(n) is produced as close a replica as possibleof x1(n). The filter readjusts itself continuously tominimize the error between x1 (n) and y (n) duringthis process. Then the output y(n) is subtracted fromthe primary input to produce the system outpute(n)=s(n)+x1(n)–y(n).This is the denoised signal.Fig.1.Adaptive Noise Cancellation SystemS(n)- source signald(n)-primary signalx1(n)-noise signalx(n)-noise reference inputy(n)-output of adaptive filtere(n)-system output signalAdaptive Filtering :Fig. 1 shows the adaptive noise cancellation setup. Inthis application, the corrupted signal passes through afilter that tends to suppress the noise while leavingthe signal unchanged. This process is an adaptiveprocess, which means it cannot require a prioriknowledge of signal or noise characteristics.Adaptive noise cancellation algorithms utilize twosignal it can vary in (sensor). One signal is used tomeasure the speech + noise signal while the other isused to measure the noise signal alone. The techniqueadaptively adjusts a set of filter coefficients so as toremove the noise from the noisy signal. Thistechnique, however, requires that the noisecomponent in the corrupted signal and the noise inthe reference channel have high coherence.Unfortunately this is a limiting factor, as themicrophones need to be separated in order to preventthe speech being included in the noise reference andthus being removed. With large separations thecoherence of the noise is limited and this limits theeffectiveness of this technique. In summary, toIn the system shown in Fig. 1 the reference input isprocessed by an adaptive filter. An adaptive filterdiffers from a fixed filter in that it automaticallyadjusts its own impulse response. Thus with theproper algorithm, the filter can operate underchanging conditions and can readjust itselfcontinuously to minimize the error signal. The errorsignal used in an adaptive process depends on thenature of the application. In noise cancelling systemsthe practical objective is to produce a system outpute(n)=s(n)+ x1 (n) –y(n) that is a best fit in the leastsquares sense to the signal s. This objective isaccomplished by feeding the system output back tothe adaptive filter and adjusting the filter through anLMS adaptive algorithm to minimize total systemoutput power. In an adaptive noise cancelling system,in other words, the system output serves as the errorsignal for the adaptive process. It might seem thatsome prior knowledge of the signal s or of the noisesx1 and x would be necessary before the filter couldbe designed, or before it could adapt, to produce thenoise cancelling s, x1 and x signal y. Assume that s,x1 , x and y are statistically stationary and have zeromeans. Assume that s is uncorrelated with x1 and x ,and suppose that x is correlated with x1 . The outpute is e=s+x1–y. (1)Squaring, one obtainse2=s2+(x1-y)2+2s(x1-y). (2)Taking expectations of both sides of (2), andrealizing that s is uncorrelated with x1 and with y,yieldsE[e2]=E[s2]+E[(x1 -y)2]+2E[s(x1 -y)]=E[s2]+E[(x1-y)2] (3)ISSN No: 2250-3536 Volume 3, Issue 3, May 2013 86
International Journal of Advanced Technology & Engineering Research (IJATER)www.ijater.comThe signal power E [s2] will be unaffected as thefilter is adjusted to minimize E[e2 ]. Accordingly, theminimum output power is mine [e2]=E[s2] +mine[(x1-y)2] (4)When the filter is adjusted so that E[e2] isminimized, E[(x1-y)2] is, therefore, also minimized.The filter output y is then a best least squaresestimate of the primary noise no. Moreover, whenE[(x1-y)2] is minimized[(e-s)2] is also minimized,since, from (1),(e-s) = (x1-y). (5)Adjusting or adapting the filter to minimize the totaloutput power is thus tantamount to causing the outpute to be a best least squares estimate of x1 the signal sfor the given structure and adjustability of theadaptive filter and for the given reference input. Theoutput z will contain the signal s plus noise. From(l),the output noise is given by(x1-y). Sinceminimizing E[e2] minimizes E[( x1-y)2] minimizingthe total output power minimizes the output noisepower. Since the signal in the output remainsconstant, minimizing the total output powermaximizes the output signal-to-noise ratio.LMS Algorithm:The LMS algorithm is a widely used algorithm foradaptive filtering. The algorithm is described by thefollowing equations:M-1 y(n) = Σwi (n)*x(n-i); (1)I = 0e(n) = d(n) – y(n (2)stability and convergence speed of the LMSalgorithm. The LMS algorithm is convergent in themean square if and only if u satisfies the condition: 0of LMSalgorithms in noise cancellation setup Fig. 1. Inputsignal is speech signal whereas Gaussian noise wasused as noise signal. The LMS adaptive filter uses thereference signal and the desired signal, toautomatically match the filter response. As itconverges to the correct filter model, the filterednoise is subtracted and the error signal should containonly the original signal. The desired signal iscomposed of colored noise and an audio signal froma .wav file. The first input signal to the adaptive filteris white noise. This demo uses the adaptive filter toremove the noise from the signal output. When yourun this demo, you hear both noise and a personrecorded voice. Over time, the adaptive filter in themodel filters out the noise so you only hear therecorded voice (Original signal).The two signals wereadded and subsequently fed into the simulation ofLMS adaptive filter. The order of the filter was set toM = 40. The parameter μ is varied. Various outputsare obtained for various step size i.e.μ = 0.002, 0.04system reaches steady state faster when the step sizeis larger. Fig.2. Original signal, Noisy signal andfilter signal for LMS step size i.e.μ= 0.002wi (n+1) = wi (n) + 2ue(n)x(n-i) (3)In these equations, the tap inputs x(n),x(n-1),……,x(n-M+1) form the elements of the referencesignal x(n), where M-1 is the number of delayelements. d(n) denotes the primary input signal, e(n)denotes the error signal and constitutes the overallsystem output. wi(n) denotes the tap weight at the nthiteration. In equation (3), the tap weights update inaccordance with the estimation error. And the scalingfactor u is the step-size parameter u controls theFigure:2 Original SignalISSN No: 2250-3536 Volume 3, Issue 3, May 2013 87
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