Adaptive Noise Cancellation using Multirate Techniques


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Adaptive Noise Cancellation using Multirate Techniques

  1. 1. International Journal of Engineering Research and DevelopmentISSN: 2278-067X, Volume 1, Issue 7 (June 2012), Adaptive Noise Cancellation using Multirate Techniques Prasheel V. Suryawanshi, Kaliprasad Mahapatro, Vardhman J. Sheth Maharashtra Academy of Engineering, Alandi (D), Pune – 412105, INDIAAbstract—This paper presents development of a new adaptive structure based on multirate filter and testing the same fordeterministic, speech and music signals. A new class of FIR filtering algorithm based on the multirate approach is proposed.They not only reduce the computational complexity in FIR filtering, but also retain attractive implementation relatedproperties such as regularity and multiply-and-accumulate (MAC)-structure. By virtue of the advantages of multirate FIRfiltering algorithm, the proposed scheme can reduce the required computational complexity and reserve the MAC structure.It is observed that the convergence rate and steady state error is improved. An application of this approach in AdaptiveNoise Canceller is considered.Keywords— Adaptive filter, Multirate filter, Adaptive Noise Cancellation I. INTRODUCTION Noise is present in virtually all signals. In some situations it is negligible; in other situations it all but obliteratesthe signal of interest. Removing unwanted noise from signals has historically been a driving force behind the development ofsignal processing technology, and it continues to be a major application for digital signal processing systems [1]. The usual method of estimating a signal corrupted by additive noise is to pass the composite signal through a filterthat tends to suppress the noise while leaving the signal relatively unchanged. Filters used for the foregoing purpose can befixed or adaptive. The design of fixed filters is based on prior knowledge of both the signal and the noise, but adaptive filtershave the ability to adjust their own parameters automatically, and their design requires little or no prior knowledge of signalor noise characteristics [2][3]. Multirate Signal Processing is the sub-area of DSP concerned with techniques that can be used to efficientlychange the sampling rates within a system. There are many applications where the signal of a given sampling rate needs tobe converted into an equivalent signal with a different sampling rate. The process of decimation and interpolation are thefundamental operations of interest in multirate signal processing. They allow the sampling frequency to be decreased orincreased without significant undesirable effects of errors such as quantization and aliasing [4][5]. The various aspects ofmultirate systems in statistical processing are reported in [6][7][8]. John Shynk [9] presents an overview of several frequency-domain adaptive filters that efficiently process discrete-time signals using block and multirate filtering techniques. A multirate adaptive filtering structure using VLSI architecture isreported in [10]. The concept of multistage multirate adaptive filters is discussed in [11][12]. The applications of theapproach in biomedical engineering [13], sub-band filtering [14], Adaptive Line Enhancement [15], Echo cancellation [16]are well proven. The work by different researchers in this direction is a motivation for working on case study of noisecancellation. The concept in [15] is extended to the Adaptive Noise Canceller (ANC) configuration, in this paper The organization of this paper is as follows; the conventional Adaptive Noise Canceller (ANC) is introduced insection 2. The LMS and RLS algorithm are also briefed. The section 3 describes the proposed structure employing multiratetechniques. Section 4 details the results for different types of signals. Section 5 concludes the paper. II. ADAPTIVE NOISE CANCELLATION The main objective in noise cancelling is to produce an optimum estimate of the noise in the contaminated signaland hence an optimum estimate of the desired signal [4]. The basic adaptive noise-canceller (ANC) schematic is shown inFig. 1. Fig. 1. Adaptive Noise Canceller (ANC) 27
  2. 2. Adaptive Noise Cancellation using Multirate Techniques A signal is transmitted to a sensor that receives the signal s plus an uncorrelated noise n0. The combined signal andnoise, s+n0, forms the primary input to the ANC. A second sensor receives a noise n1 which is uncorrelated with the signalbut correlated in some unknown way with the noise n0. This sensor provides the reference input to the ANC. The noise n1 isfiltered to produce an output y that is a close replica of n0. This output is subtracted from the primary input s+n0 to producethe output, s+n0 – y. In the system shown in Fig. 1, the reference input is processed by an adaptive filter that automatically adjusts itsown impulse response through a least-squares algorithm such as LMS that responds to an error signal dependent on thefilter‘s output. Thus with the proper algorithm, the filter can operate under changing conditions and can readjust itselfcontinuously to minimize the error signal. In noise-cancelling systems the practical objective is to produce a system output, s+n0–y, that is a best fit in theleast-squares sense to the signal s. This objective is accomplished by feeding the system output back to the adaptive filterand adjusting the filter through an adaptive algorithm to minimize the total system output power. Thus in an adaptive noise-cancelling system, the system output serves as the error signal for the adaptive process.A. LMS Algorithm The LMS algorithm, developed by Widrow and his co-workers [2] is based on the steepest descent algorithmwhere the weight vector is updated from sample to sample and it does not require prior knowledge of the signal statistics, butinstead uses their instantaneous estimates. The weights obtained by the LMS algorithm are only estimates, but theseestimates improve gradually with time as the weights are adjusted and the filter learns the characteristics of the signal.Eventually, the weights converge. The condition for convergence is 1 0< μ> (1) λmax where λ is the maximum eigen value of the input data covariance matrix. The implementation of LMS algorithm maxinvolves iterative computations involving,  N 1 filter output; nk   wk (i) xk i (2) i 0  error estimate; ek  yk  nk (3) update of filter weights; wk 1 (i)  wk (i)  2 ek xk i (4) The simplicity of the LMS algorithm and ease of implementation, evident from (2), (3) and (4), makes it thealgorithm of first choice in many real-time systems. The LMS algorithm requires approximately 2N+1 multiplications and2N+1 additions for each new set of input and output samples. Most signal processors are suited to the mainly multiply-accumulate arithmetic operations involved, making a direct implementation of the LMS algorithm attractive.B. RLS Algorithm The RLS (recursive least squares) algorithm is another algorithm for determining the coefficients of an adaptivefilter. In contrast to the LMS algorithm, the RLS algorithm uses information from all past input samples (and not only fromthe current tap-input samples) to estimate the (inverse of the) autocorrelation matrix of the input vector [9]. The RLS algorithm is based on the well-known least squares method. With recursive least squares algorithm, theestimates of Wk can be updated for each new set of data acquired without repeatedly solving the time-consuming matrixinversion directly. A suitable RLS algorithm can be obtained by exponentially weighting the data to remove gradually theeffects of old data on Wk and to allow the tracking of slowly varying signal characteristics. Thus Wk  Wk 1  Gk ek (5) 1  Pk  P  Gk xT (k ) Pk 1  (6)   k 1  Pk 1 x(k ) Gk  (7) k ek  yk  xT (k ) Wk 1 (8)  k    xT (k ) Pk 1 x(k ) (9) 28
  3. 3. Adaptive Noise Cancellation using Multirate Techniques 1 Pk is essentially a recursive way of computing the inverse matrix  X k X k  T . The argument k emphasizes the  fact that the quantities are obtained at each sample point. The typical value of  (forgetting factor) is between 0.98 and 1.Smaller values assign too much weight to the more recent data, which leads to wildly fluctuating estimates. The RLS algorithm is computationally more complex than the LMS algorithm. However, due the recursiveupdating, the inversion of matrix is not necessary (which would be a considerably higher computational load). The RLSalgorithm typically shows a faster convergence compared to the LMS algorithm. Other advantages are that it produces aweight vector estimate only at the end data sequence III. PROPOSED SCHEME The proposed structure of adaptive noise cancellation scheme using multirate technique is shown in Fig. 2. Startingwith the basic framework for Adaptive filters, a structure has been built eliminating the basic faults arising likecomputational complexities, aliasing and spectral gaps. Fig. 2. Proposed Structure of ANC with Multirate Technique The H0, H1, Ha are the analysis filters and G0, G1 are the reconstruction filters. The decimation and interpolationfactors have been taken as ‗2‘ as the number of sub-bands are 2. The proposed scheme achieves a lower computationalcomplexity, and this design ensures no aliasing components in the output of the system. The system consists of two mainsub-bands and an auxiliary sub-band. The auxiliary sub-band contains the complement of the signals in the main sub-band. In the fig. 2, Ha(z) is the analysis filter for the auxiliary sub-band and H0(z) and H1(z) are the analysis filters for themain bands. G0(z) and G1(z) are reconstruction filters for the main bands. These filters are related to each other as; H1 ( z)  H0 ( z) (10) G0 ( z)  2 H1 ( z) (11) G1 ( z)   2 H0 ( z) (12) H a ( z )  z m   H 02 ( z )  H12 ( z)  (13)   The coefficients of all filters are calculated and the scheme is tested for different input types. IV. RESULTS AND ANALYSIS The proposed scheme using 2 bands with decimation factor of 2, is tested for deterministic signal, speech andmusical signals. The results are compared with conventional ANC.A. Deterministic Signal For deterministic signal, 128 samples of signal and noise are considered. Fig. 3 to Fig. 6 shows the convergenceresults of the proposed scheme and conventional ANC for a deterministic signal of 10sin(1500t) and noise of 10 sin(312t). 29
  4. 4. Adaptive Noise Cancellation using Multirate Techniques Fig. 3. Deterministic signal – Conventional ANC Fig. 4. Input and output spectra – Conventional ANC Fig. 5. Deterministic signal – Proposed Scheme Fig. 6. Input and output spectra – Proposed Scheme It is evident that, the output of the noise canceller exactly matches the desired signal. The update algorithm used isLMS. The periodogram clearly demonstrates the removal of noise.B. Speech Signal For speech signal, 32000 samples with sampling frequency 8 KHz are considered. The noise signal is a sine waveof 312 Hz. The Algorithm used is LMS. Fig. 7 to Fig. 10 shows the results of the proposed scheme and conventional ANCfor a speech signal. Fig. 7. Speech signal – Conventional ANC Fig. 8. Spectra of Speech – Conventional ANC 30
  5. 5. Adaptive Noise Cancellation using Multirate Techniques Fig. 9. Speech Signal – Proposed Scheme Fig. 10. Spectra of Speech signal – Proposed SchemeC. Music Signal The music signal considered is 8000 samples of piano along with 8000 samples of tabla taken as noise. TheAlgorithm used is LMS. Fig. 11 to Fig. 14 shows the results of the proposed scheme and conventional ANC for a musicsignal (piano + tabla). Fig. 15 to Fig. 16 shows the results of the proposed scheme for a music signal of closely matchedfrequencies (guitar + violin). Fig. 11. Music signal (Piano + Tabla) Fig. 12. Spectra of Music signal (Piano + Tabla) Conventional ANC Conventional ANC 31
  6. 6. Adaptive Noise Cancellation using Multirate Techniques Fig. 13. Music signal (Piano + Tabla) Fig. 14. Spectra of Music signal (Piano + Tabla) Proposed Scheme Proposed Scheme Fig. 15. Music signal (Guitar + Violin) Fig. 16. Spectra of Music signal (Guitar + Violin) Proposed Scheme Proposed Scheme The results are encouraging for the proposed multirate adaptive scheme and are indicative of quite less time(approximately one-fourth) for computation as compared to the conventional ANC structure. Additionally, signals withclosely matched frequencies (eg. violin and guitar) can be effectively segregated using the proposed scheme, which is notpossible with the conventional ANC configuration.The Table 1 shows the computation time for conventional ANC and the proposed scheme. TABLE I: COMPUTATION TIME REQUIREMENT Input Signal Conventional ANC Proposed Scheme Deterministic 16 ms 4.2 ms Speech 4.453 sec 1.485 sec Musical 0.18441 sec 0.134881 sec V. CONCLUSIONS This paper proposes a new adaptive noise cancellation structure based on multirate techniques. Noise Cancellationis chosen as the application because noise is one of the main hindering factors that affect the information signal in anysystem. Noise and signal are random in nature. As such, in order to reduce noise, the filter coefficients should changeaccording to changes in signal behaviour. The adaptive capability will allow the processing of inputs whose properties areunknown. Multirate techniques can be used to overcome the problem of large computational complexity and slowconvergence rate. The simulations and experiments demonstrate the efficacy of the proposed structure. REFERENCES [1]. Britton C. Rorabaugh, Digital Signal Processing Primer, New Delhi, India: TMH, 2005. [2]. Bernard Widrow and Samuel D. Stearns, Adaptive Signal Processing, 3rd Indian Reprint, New Delhi, India: Pearson Education, 2004. [3]. Simon Haykin, Adaptive Filter Theory, 4th ed., New Delhi, India: Pearson, 2003. [4]. Emmanuel C. Ifeachor and Barrie W. Jervis, Digital Signal Processing, 2nd ed., New Delhi, India: Pearson, 2002. [5]. P. P. Vaidyanathan, ―Multirate Digital Filters, Filter Bank, Polyphase Networks and Applications: A Tutorial‖, Proceedings of the IEEE, vol.78, no. 1, pp. 56-91, Jan. 1990. 32
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