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  1. 1. Prof. Vijaya sughandhi, Prof. D.K.Rai / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.893-896 Statistical Evaluation In Speech Processing Techniques Prof. Vijaya sughandhi1 Prof. D.K.Rai2 Dept. of Electrical & Elex. Engg. Dept. of Electrical & Elex. Engg. Shri VaishnavSM Institute of Tech. Shri VaishnavSM Institute of Tech. & science, Indore (M.P.)-India & science, Indore (M.P.)-IndiaABSTRACT The objective of this paper is to generate II. BACKGROUNDa reconstructed output speech signal from the The term speech processing basically refersinput signal involving the application of a filter to the scientific discipline concerning the analysisestimation technique. In this paper, filter is used and processing of speech signals in order to achieveto estimate the parameters represented in the the best benefit in various practical scenarios [2]. Thestate-space domain, in which the speech signal is field of speech processing is, at present, undergoing amodeled as such. rapid growth in terms of both performance and The results of this speech coding applications. This is stimulated by the advances beingtechnique are demonstrated and obtained with the made in the field of microelectronics, computationhelp of MATLAB. Accurate estimations by the and algorithm design [3].filter on speech is simulated and presented.Comparison between the assigned values and the Samplingestimated values of the parameters is described. The purpose of sampling is to transform anThe reconstruction of speech and the input speech analog signal that is continuous in time to a sequenceis also compared for error estimations. of samples discrete in time. The signals we use in theKey words: filter, speech coding technique. real world, such as our voices, are called "analog" signals. In order to process these signals in1. INTRODUCTION computers, most importantly it must be converted to Speech processing has been a growing and "digital" form. While an analog signal is continuousdynamic field for more than two decades and there is in both time and amplitude, a digital signal is discreteevery indication that this growth will continue and in both time and amplitude. Since in this thesis,even accelerate. During this growth there has been a speech will be processed through a discrete Kalmanclose relationship between the development of new filter, it is necessary for converting the speech signalalgorithms and theoretical results, new filtering from continuous time to discrete time, hence thistechniques are also of consideration to the success of process is described as sampling.speech processing. One of the common adaptivefiltering techniques that are applied to speech is the The value of the signal is measured atWiener filter. This filter is capable of estimating certain intervals in time. Each measurement iserrors however at only very slow computations. On referred to as a sample. Once the continuous analogthe other hand, the Kalman filter suppresses this speech signal is sampled at a frequency f, thedisadvantage. resulting discrete signal will have more frequency According to [1], Kalman filter is so popular components than the analog signal. To be precise, thein the field of radar tracking and navigating system is frequency components of the analog signal arethat it is an optimal estimator, which provides very repeated at the sample rate. Explicitly, in the discreteaccurate estimation of the position of either airborne frequency response they are seen at their originalobjects or shipping vessels. Due to its accurate position, and also centered around +/- f, and +/- 2 f,estimation characteristic, electrical engineers are etc.picturing the Kalman filter as a design tool for The signal still preserve the information, it isspeech, whereby it can estimate and resolve errors necessary to sample at a higher rate greater thanthat are contained in speech after passing through a twice the maximum frequency of the signal. This isdistorted channel. Due to this motivating fact, there known as the Nyquist rate. The Sampling Theoremare many ways a Kalman filter can be tuned to suit states that a signal can be exactly reconstructed if it isengineering sampled at a frequency f, where f > 2fm where fm is maximum frequency in the signal.Applications such as network telephony and evensatellite phone conferencing. III. PROPOSED METHODOLOGY From a statistical point of view, many signals such as speech exhibit large amounts of 893 | P a g e
  2. 2. Prof. Vijaya sughandhi, Prof. D.K.Rai / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.893-896correlation. From the perspective of coding or signal Yk. That is in order to construct Yk, we willfiltering, this correlation can be put to good use [6]. need matrix X that contains the Kalman coefficientsThe all pole, or autoregressive (AR), signal model is and the white noise, wk which both are obtained fromoften used for speech. From [4], the AR signal model the estimation of the input signal. This information isis introduced as: enough to determineHHk-1.yk = a1yk-1 + a2yk-2 + ……. + aNyk-N + wk (3.1)where, Wherek = Number of iterations;yk= current input speech signal sample; HHk-1= 3.10yk=(N-1)th sample of speech signal;aN =Nth Kalman filter coefficient;and wk = excitation sequence (white noise). Thus, forming the equation (3.10) mentioned above.In order to apply Kalman filtering to the speechexpression shown above, it mustbe expressed in state IV. RESULTSspace form as This approach is to prove that Kalman filterHk = X Hk-1 + Wk (3.2) functions properly in MATLAB 7. Reconstructedyk = g Hk (3.3) accurate sound output are shown in fig.4.1.The results shown below from Fig 4.2 to Fig 4.6, the X is the system matrix, Hk consists of the Kalman filter generates a very close set ofseries of speech samples; Wk is the excitation vector coefficients, which are similar to those, selectedand g, the output vector. The reason of (k-N+1)th above in (4.2). From the following results, accurateiteration is due to the state vector, Hk, consists of N estimation of the coefficients took several hundredssamples, from the kth iteration back to the(k-N+1)th of iterations in order to stabilize to the required value.iteration. The reason for this is that Kalman filter works in a loop fashion. In order to obtain a more accurate The above formulations are suitable for the estimate, it will need to go through more “predict”Kalman filter. As mentioned in the previous chapter, and “correct” proceduresthe Kalman filter functions in a looping method. 0.4 reconstruct output of sound1Referring to [5] as a guide in implementing Kalman 0.3filter to speech, we denote the following steps withinthe loop of the filter. Define matrix HT k-1 as the row 0.2vector: 0.1HTk-1 = -[yk-1 yk-2 … yk-N] (3.4) 0 v(k)and zk = yk. Then (3.1) and (3.4) yield -0.1 zk = HTk-1 Xk + wk ( 3.5) -0.2 where Xk will always be updated accordingto the number of iterations, k. when the k = 0, the -0.3matrix Hk-1 is unable to be determined. However, -0.4when the time zk is detected, the value in matrix Hk-1 -0.5 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000is known. The above purpose is thus sufficient Number of Iterationsenough for defining the Kalman filter, which consists Fig. 4.1 Output of reconstructed signalof: Estimated FilterXk = [ I – KkHTk-1] Xk-1 + Kk zk (3.6) 0Where I= Identity matrixwith -0.1Kk = Pk-1Hk-1[ HTk-1Pk-1 Hk-1 + R ]-1 (3.7)where Kk is the Kalman gain matrix, Pk-1 is the a -0.2priori error covariance matrix,R is measurement -0.3noise covariance.andPk = Pk-1 - Pk-1 Hk-1 [HTk-1 Pk-1 Hk-1 + R]-1.HTk-1Pk-1 + Q -0.4 XX(1,k)where Pk is the a posteriori error covariance matrix, -0.5and Q is identity matrix.Thereafter the reconstructed speech signal, Yk after -0.6Kalman filtering will be formed in a manner similarto (3.1): -0.7Yk = a1Yk-1 + a2Yk-2 + ……. + aNYk-N + wk (3.9) -0.8Since the value of Yk is the input at the beginning ofthe process, there will be no problem forming HTk-1. -0.9 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000In that case a question rises, how is Yk formed? The Number of Iterationsparameters wk and {ai}i=1 Nare determined from Fig. 4.2 First coefficient of filterapplication of the Kalman filter to the input speech 894 | P a g e
  3. 3. Prof. Vijaya sughandhi, Prof. D.K.Rai / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.893-896 Estimated Filter 0.25 Estimated Filter 0.05 0.2 0 0.15 -0.05 0.1 -0.1 0.05 -0.15XX(2,k) XX(5,k) 0 -0.2 -0.25 -0.05 -0.3 -0.1 -0.35 -0.15 -0.4 -0.2 -0.45 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 -0.25 Number of Iterations 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Number of Iterations Fig. 4.6 Fifth coefficient of filter Fig. 4.3 Second coefficient of filter V. CONCLUSION Estimated Filter In this paper, an implementation of 0.1 employing Kalman filtering to speech processing had been developed. As has been previously mentioned, 0 the purpose of this approach is to reconstruct an output speech signal by making use of the accurate -0.1 estimating ability of the Kalman filter. Simulated results from the previous section had proven that the -0.2 Kalman filter has the ability to estimate accurately. XX(3,k) -0.3 Acknowledgment This author thanks to their family and -0.4 friends for their motivation support and encouragement. -0.5 Reference: [1] M.S. Grewal and A.P. Andrews, Kalman -0.6 Filtering Theory and Practice Using MATLAB 2nd eition, John Wiley & Sons, -0.7 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Canada, 2001, pp 15-17 Number of Iterations [2] R. P. Ramachandran and R. Mammone, Fig. 4.4 Third coefficient of filter Modern Methods of Speech Processing, Kluwer Academic Publishers, Massachusetts, USA, 1994. Estimated Filter [3] A.N. Ince, Digital Speech Coding, Kluwer 0.8 Academic Publishers, Massachusetts, USA, 0.7 1992. 0.6 [4] S. Crisafulli, J.D. Mills, and R.R Bitmead, “Kalman Filtering Techniques in Speech 0.5 Coding”. In Proc. IEEE International 0.4 Conference on Acoustics, Speech, and XX(4,k) 0.3 Signal Processing, San Francisco, March 0.2 1992. [5] B.D.O. Anderson and J.B. Moore, “The 0.1 Kalman Filter,” Optimal Filtering, Prentice 0 Hall Inc., Englewood Cliffs, N.J., 1979, pp. -0.1 50-52. -0.2 [6] C. R. Watkins, “Practical Kalman Filtering 0 500 1000 1500 2000 2500 3000 Number of Iterations 3500 4000 4500 5000 in Signal Coding”, New Techniques in Signal Coding, ANU, Dec 1994. Fig. 4.5 Fourth coefficient of filter 895 | P a g e
  4. 4. Prof. Vijaya sughandhi, Prof. D.K.Rai / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.893-896 Ms.Vijaya Sugandhi received the B.E. .degree and M.E.(digital techniques &instrumentation) Degree with in Electrical engineering in 2006 and 2011 both from Rajiv Gandhi Technical University, Bhopal, Madhypradesh, India Mr. Dev Kumar Rai received the B.E. .degree (with Hon’s) and M.E.(Power Electronics) Degree with in Electrical engineering in 2004 and 2010 both from Rajiv Gandhi Technical University, bhopal, Madhyapradesh, India 896 | P a g e