Implementation of Adaptive Filters on TMS320C6713 using LabVIEW A Case Study

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1 Indian Journal of Science and Technology, Vol 8(22), DOI: /ijst/2015/v8i22/79197, September 2015 ISSN (Print) : ISSN (Online) : Implementation of Adaptive Filters on TMS320C6713 using LabVIEW A Case Study Thadigotla Venkata Subbareddy *, Saureddy Omkar Reddy, Chakka Sri Harsha Kaushik and V. Elamaran Department of ECE, School of EEE, SASTRA University, Thanjavur , Tamil Nadu, India; ssubbareddy.984@gmail.com, omkarreddy.s@gmail.com, sriharshakaushik.chakka@gmail.com, elamaran@ece.sastra.edu Abstract Adaptive filters are playing a vital role in signal processing and communication filed of engineering for the purpose of filtering the unwanted signal, signal denoising, signal enhancement, etc. The main characteristic of the adaptive filter is the adjustment of filter coefficients dynamically with respect to the input signal which helps a lot in signal processing applications. This study main focus on implementing such adaptive filters on digital signal processors. The adaptive filtering algorithms such as Least Mean Square (LMS) algorithm and Normalized LMS (NLMS) algorithms are implemented with TMS320C6713 floating-point DSP processor using LabVIEW environment in real time. To test the functionality of the algorithms, the sinusoid signal is added with noisy and applied as an input the filter and the resultant denoising output is obtained with both the algorithms. We implement it with TMS320C6713 floating-point Digital Signal Processor using LabVIEW environment in real time. Our objective is to reduce or filter the noise using these algorithms and obtain the performance metrics like peak output, Mean Square Error (MSE), Peak Signal-to-Noise Ratio (PSNR) as a part of simulation results. The PSNR produced by the NLMS algorithm is obtained as is very high as compared with produced by the LMS algorithm. Interfacing the TMS320C6713 DSP board with the LabVIEW application is done using the Code Composer Studio software tool. This study focuses the principle of adaptive filters by implementing the Least Mean Square (LMS) algorithm and Normalized LMS algorithms and can be further extended with Kalman filters too. er. Keywords: Adaptive Filters, Code Composer Studio, LabVIEW, LMS Algorithm, NLMS Algorithm, TMS320C Introduction Digital signal processing is a major part of recent advancements such as filtering of noise, prediction of voice and system identification. Standard signal processing methods are inadequate to solve these issues in real-time. Analog signal processing was used initially to band limit signals thus avoiding noise from frequencies outside the band. This band limiting and restricting is known as filter. Due to the increasing need for accurate data, various signal processing techniques that reduce noise within the permitted band are being used. Thus digital signal processing became advantageous. One of the most highly used techniques is adaptive filtering. Adaptive filtering techniques use an adaptive algorithm to predict the noise and subtract them from a noisy signal. Thus it promotes accurate and timely convergent solutions. Noises generally vary in realtime and so a constant pattern like additive white Gaussian noise cannot be directly considered for noise reduction or removal. Changes in weather conditions, density of air and many other causes can vary the noise and thus it is highly random in nature. They can only depend on a few previous values of noise as change occurs in a continuum. Thus adaptive filter turns very advantageous as it depends on a few recent values of the input signal and noise to study a pattern and adapt to it 1,2. There are various types of filters that produce outputs based on a few recent inputs. A simple filter like Finite Impulse Response filter takes some recent values and multiplies with the filter co-efficient to produce a filtered *Author for correspondence

2 Implementation of Adaptive Filters on TMS320C6713 using LabVIEW A Case Study response. The filter s co-efficient are determined using an adaptive algorithm thus making an adaptive Finite Impulse Response filter. The number of recent inputs to be considered for making the filter is pre-determined by the user. This is termed as taps. The adaptive algorithm determines the amount of error correction that can be possibly done. The Wiener-Hopf equation can remove noise to a very great effect but the processing involves inversion of a matrix and determining the correlation matrix which takes more time and thus can process only with a lesser number of taps. Simpler and moderately efficient algorithms replaced complicated and time-consuming algorithms. One such algorithm is the Least Mean Square (LMS) gradient approximation algorithm. The least mean square involves simple mathematical operations like addition, subtraction and multiplication thus making the processing faster and easier. This algorithm is more realistic and practical in nature 3. Though the LMS algorithm provides coefficients to update the output signal, they cannot be used directly as the amount of learning from the error is very high. Directly learning from the coefficients can cause abnormal spikes and very fast movement towards the desired signal. Thus a learning factor is introduced to obtain a partial part of the new coefficients thus reducing the spikes. This learning factor determines the rate of convergence. The LMS algorithm was later improvised to make an adaptive learning factor. This algorithm came to be known as Normalized Least Mean Square (NLMS) algorithm. 2. Adaptive Filters adaptive filter requires extra information about the environment that is introducing the noise. Also a reference or desired signal is to be known so as to successfully approximate the input signal towards an output that has lesser noise. The desired signal can be determined only based on the application where the signal is used 5,6. The general structure of an adaptive filter is shown in Figure 1. There are two main parts in the configuration. The Adaptive filter has the non-fixed coefficients which will filter the noisy input signal, x(k) to generate a signal of lesser noise as y(k). The adaptive algorithm takes the error signal, e(k) as input and modifies the weights, w(k) accordingly 7,8. The difference is the error between the desired output d(k) and y(k), is expressed as follows: e(k) = d(k) y(k) (1) For an FIR filter, Y(k) can be defined as the product of the filter coefficients, W(k) and the noisy input, X(k) and is denoted as follows: Y(k) = W T (k) X(k) (2) Here, X(k) represents an array of N recent inputs and W(k) represents an array of N coefficients. The T represents the matrix transpose function. There are N taps in the FIR filter. 3. Least Mean Square Algorithm Least Mean Square (LMS) algorithm is the simplest adaptive algorithm that uses simple additive property on filter coefficients to update them. They variation depends on the previous input signal and error co-efficient 14.They can be represented using the following Equation. An adaptive filter is a type of filter that has time variant filter coefficients. It is used when constant specifications are unknown or such specifications are not satisfactory. Thus it generally has non-linear characteristics 4. But considering the adaptive filter equation at a particular instant of time, the output is a linear function of the corresponding input signals. In a fixed filter (non-adaptive), a thorough study about the input and reference signals are needed to design the closest possible filter to meet maximum performance. But in real-time, the environment is varying and so is the noise affecting the signal. Here adaptive filter poses as an optimal solution. Adaptive filter updates all its parameters through simple algorithms using environmental variables in real-time. Thus it performs a data-driven filtering operation. The cases where adaptive filters are used are when the parameters are time-variant or unavailable. Thus an Figure 1. General adaptive filter structure. w(k + 1) = w(k) µ e(k) x(k) (3) 2 Vol 8 (22) September Indian Journal of Science and Technology

3 Thadigotla Venkata Subbareddy, Saureddy Omkar Reddy, Chakka Sri Harsha Kaushik and V. Elamaran Where e(k) is the error signal, x(k) is the previous input signal and µ is convergence or learning factor. The new co-efficient w(k + 1) can be obtained and thus the error considerably reduced in successive steps 6,9. The updating is carried out till the derivate of Mean square error is zero. The convergence factor (µ) is determined by the largest Eigen value of the auto-correlation matrix (λ max ) of the input signal. The convergence factor should be less than the inverse of λ max i.e. µ < 1/λ max. For a value of convergence factor (µ) greater than inverse of maximum Eigen value (λ max ), the output signal will not converge and thus produce spikes. Since convergence factor is predetermined, they would not introduce any computational complexity 10,11. Thus the LMS-FIR filter is the simplest and fastest filter. This algorithm is implemented using LabVIEW software tool 12,13 and is depicted in Figure Normalised Least Mean Square Algorithm One of the drawbacks of the basic LMS algorithm is that it is sensitive to the scaling of its input. This makes the choice of the convergence factor (µ) very difficult and thus the stability of the algorithm. To be on the safer side, very small value of convergence factor has to be used thus making the convergence at a slower rate. The Normalized Least Mean Square (NLMS) takes care of this drawback by making an adaptive convergence factor. The adaptive convergence factor (µopt) is given by the following Equation: µ opt = β / [x 2 [n] + δ] (4) Here β is the normalized step size which is a value between 0 and 2, δ is a factor used to avoid divide by zero. Thus the co-efficient update Equation becomes w(k+1) = w(k) - µ opt e(k) x(k) (5) The normalization of step size reduces sensitivity to the spread of the Eigen value of the auto-correlation of the input signal. The direction of the tap coefficients still remain in the direction of steepest descent as it was in the LMS algorithm. The convergence characteristics are far superior to this algorithm and thus provide a better output. A normalized LMS algorithm is implemented and is depicted in Figure Simulation Results Analysis of the performance between these two filters has to be determined by using standard performance metrics. LabVIEW is used as a pertinent tool for this kind of signal processing application study. The reduction in noise is to be analyzed. The SNR is the simplest metric for such an analysis. So the MSE and consequently the PSNR are determined to distinguish the performance and thus provide a greater understanding on the results obtained. Mean Square Error (MSE) is determined by finding the error for an obtained set of values by subtracting every value from their mean value and squaring them and then dividing by the total number of values in the set, as depicted as follows: MSE = n 1 n 2 i= 0 e () i (6) where, n being the number of values in the set and e(i) representing the error. Figure 2. LMS Algorithm using LabVIEW. Figure 3. NLMS Algorithm using LabVIEW. Vol 8 (22) September Indian Journal of Science and Technology 3

4 Implementation of Adaptive Filters on TMS320C6713 using LabVIEW A Case Study PSNR is very often analyzed for measuring the quality of the signal and is determined by the logarithm of ratio of square of Maximum output signal to the Mean Square Error as expressed as follows: PSNR = 10 log 10 (MAX I2 /MSE) (7) Where MAX I is the maximum output signal and MSE represents the Mean Square Error. Figure 4 shows LabVIEW model in which the channel produces noise. Block diagrams have been made for Least Mean Square and Normalized Least Mean Square algorithm with FIR filters. These block diagrams are shown in Figure 5 and 6. Performance characteristics like PSNR and MSE are calculated based on the obtained values like Output signal strength and the error signal. The calculated PSNRs are compared to know the real-time effects of various algorithms in TMS320C6713 DSP Processor and the results are depicted in the Table 1. The corresponding noisy and noise cancelled output waveforms are shown in Figure 7 and 8 using LMS algorithm and NLMW algorithm respectively. Figure 6. NLMS algorithm using TMS320C6713. Table 1. Peak Signal to Noise Ratio (PSNR) Results Figure 4. Noise generation using LabVIEW. Algorithm Peak Output MSE PSNR LMS NLMS Figure 5. LMS algorithm using TMS320C6713. (a) 4 Vol 8 (22) September Indian Journal of Science and Technology

5 Thadigotla Venkata Subbareddy, Saureddy Omkar Reddy, Chakka Sri Harsha Kaushik and V. Elamaran 6. Conclusion and Future Work (b) Figure 7. (a) Noisy input signal (LMS). (b) Noiseless output (LMS). (a) (b) Figure 8. (a) Noisy input signal (NLMS) and (b) Noiseless output (NLMS). The trend towards good quality signal and data is increasing especially for audio, video and also for medical signals. Clarity in audio and video gives a comfortable entertainment. Also the need for better quality signals in medical diagnosis helps doctors to diagnose diseases easily and reduces medical errors. Electro Encephalogram (EEG) is a major medical application for adaptive noise cancellers. It also has military applications like over-riding jammers and obtains data accurately. This work can be further extended for medical signals i.e., for both one-dimensional and two-dimensional signals. 7. References 1. Chaitanya KS. Implementation of reconfigurable adap tive filtering algorithms. Proceedings in International Conference on Signal Processing Systems; Singapore May. p Velazquez LJ, Garcia JCS, Meana HP. Adaptive filters with codified error LMS Algorithm. Telecommunications and Radio Engineering. 2006; 65(6-10): Saxena G. Real time implementation of adaptive noise cancellation. Proceedings in IEEE Conference on Electro/ Information Technology; Ames, IA May. p Perez E, Shearman S. LabVIEW DSP A hands on educational platform. Proceedings in IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education; 2009 Jan. p Das M. An improved adaptive wiener filter for de-noising and signal detection. Proceedings in Signal and Image Processing; Hawaii, USA p Haykin S. Adaptive Filter Theory. Upper Saddle River, NJ: Prentice Hall; Vazquez BLS, Garcia IJC, Sanchez GJC. Description of adaptive fuzzy filtering using the DSP TMS320C6713. Proceedings in IEEE International Midwest Symposium on Circuits and Systems; Cancun Aug. p Tavares RJA, Escamilla HE, Sanchez GJC. DSP-based oversampling adaptive noise canceller for background noise reduction for mobile phones. Proceedings in 22nd International Conference on Electrical Communications and Computers (CONIELECOMP); Cholula, Puebla Feb. p LMS Adaptive Filter. Lattice Semiconductor Corporation; Elamaran V, Aswini A, Niraimathi V, Kokilavani D. FPGA implementation of audio enhancement using adaptive Vol 8 (22) September Indian Journal of Science and Technology 5

6 Implementation of Adaptive Filters on TMS320C6713 using LabVIEW A Case Study lms filters. Journal of Artificial Intelligence Dec; 5(4): Ozbay Y, Kavsaoglu AR. An optimum algorithm for adaptive filtering on acoustic echo cancellation using TMS320C6713 DSP. Digital Signal Processing Jan; 20(1): Kehtarnavaz N. Digital Signal Processing System-Level Design using LabVIEW. Elsevier Publsihers; Clark CL. LabVIEW Digital Signal Processing and Digital Communications. McGraw-Hill Publishers; Bhotto MZA, Antoniou A. A family of shrinkage adaptivefiltering algorithms. IEEE Transactionson Signal Processing Apr; 61(7): Vol 8 (22) September Indian Journal of Science and Technology