In this paper, we illustrate the use of adaptive algorithms to time varying conditions on the linear filter. We explain the Least Mean Square Algorithm which is based upon the stochastic gradient algorithm. Using this algorithm in SIMULINK on windows platform, we demonstrate the use of LMS algorithm to get the desired signal from noisy signal. Estimation can be done in three ways namely filtering, smoothing and prediction, out of which smoothing gives good results. The LMS algorithm is a linear adaptive filtering algorithm, which in general has two processes associated with it filtering and adaptive process.
The LMS (Least-Mean-Square) algorithm which is a linear adaptive filtering algorithm, works under two basic processes namely a filtering process and an adaptive process. Adaptive process is used to provide a mechanism for the adaptive control of an adjustable set of parameters used in filtering process.
Keywords- Adaptive filters, LMS Algorithm, Simulink, Estimation theory, noise.
[...] USE OF C6713 DSK FOR IMPLEMENTATION OF LMS ALGORITHM The C6713 DSK has a TMS320C6713 DSP onboard that allows full-speed verification of code with Code Composer Studio. The C6713 DSK provides: A USB Interface SDRAM and Flash ROM An analog interface circuit for Data conversion (AIC) An I/O port Embedded JTAG emulation support Connectors on the C6713 DSK provide DSP external memory interface (EMIF) and peripheral ignals that enable its Voltages 8-kHz 96-kHz Sampling-Frequency Support Software Control Via TI McBSP-Compatible Multiprotocol Serial Port I 2 C-Compatible and SPI-Compatible Serial-Port Protocols Glueless Interface to TI McBSPs Audio-Data Input/Output Via TI McBSP-Compatible Programmable Audio Interface I 2 S-Compatible Interface Requiring Only One McBSP for both ADC and DAC Standard I 2 MSB, or LSB Justified-Data Transfers 16/20/24/32-Bit Word Lengths configure the board by reading and writing to the CPLD The TMS320C6713™ DSP compose the floating-point DSP generation in the TMS320C6000™ DSP platform. [...]
[...] As a direct consequence of the application of a recursive algorithm whereby the parameters of an adaptive filter are updated from one iteration to the next, the parameters become data dependent. IX. IMPLEMENTATION OF LMS ALGORITHM ON C6713 DSK Using C6713 DSK we implemented the LMS algorithm, which shows that after finite time, the noise signal is removed from the original signal, and only desired signal remains at the output of LMS filter. IX. CONCLUSION Fig.2. TMS320C6713 DSK Overview Block Diagram registers. [...]
[...] In other words, a random signal is not predictable, it never repeats itself, and we cannot find a mathematical formula that provides its values as a function of time. As a result, random signals can only be mathematically described by using the theory of stochastic processes Filtering III. KINDS OF ESTIMATION Extraction of a information about a quantity of interest at time t by using data measured upto and including t. Posteriori form of estimation is used in smoothing. Posteriori means after the fact. [...]
[...] LMS algorithm is an important member of the family of stochastic gradient algorithms. The LMS algorithm has features like simplicity & does not require measurements of the pertinent correlation functions, nor it require matrix inversion. An Estimator or filter is a system that is designed to extract the information about a prescribed quantity of interest from described mathematically by using the theory of probability, random variables, and stochastic processes. However, in practice we deal with random signals by using statistical techniques. [...]
[...] The result so obtained When the value of is zero, it is optimum filter. When the value of is 1 it has no agreement between filter output & which is worst possible condition. VII. STRUCTURE AND OPERATION OF THE LEAST MEAN SQUARE ALGORITHM The LMS algorithm is a linear adaptive filtering algorithm , which in general has two processes associated with it. A filtering process: Computation of output of a linear filter in response to input signal and generation of estimation error by comparing this output with desired response. [...]
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