A full programming routine written in MATLAB software environment is provided for replications and further research applications. We present some numerical applications forecasts for the Gross Domestic Product growth rate of UK and Italy, forecasts for S&P 500 stock index returns and finally we examine the day of the week effect of FTSE 100 for a short period. In this example, we will first solve the deconvolution problem using the least-squares, steepest descent and conjugate gradient algorithms. Appropriate input data to exercise the adaptation process. In this example, the filter designed by fircband is the unknown system. An unknown system or process to adapt to. Call: =wiener(W,sigmav2) Input arguments: W =eigenvalue spread, dim 1x1 sigmav2 =variance of the additive noise source, dim 1x1 Output arguments: Jmin =minimum MSE obtained by the Wiener filter, dim 1x1 R =autocorrelation matrix, dim 11x11 p =cross-correlation vector, dim 11x1 wo =optimal filter, dim 11x1 Choose the remaining parameters according to Haykin chapter 9.7.In this paper we present a very brief description of least mean square algorithm with applications in time-series analysis of economic and financial time series. In this example, set the Method property of dsp.LMSFilter to LMS to choose the LMS adaptive filter algorithm.

Solution and Jmin for computer exercise 2.4. Optimal filter function =wiener(W,sigmav2) %WIENER Returns R and p, together with the Wiener filter Adaptive Signal Processing 2010 Program code LMS function =lms(mu,M,u,d) % Call: % =lms(mu,M,u,d) % % Input arguments: % mu = step size, dim 1x1 % M = filter length, dim 1x1 % u = input signal, dim Nx1 % d = desired signal, dim Nx1 % % Output arguments: % e = estimation error, dim Nx1 % w = final filter coefficients, dim Mx1 %inital values: 0 w=zeros(M,1) %number of samples of the input signal N=length(u) %Make sure that u and d are column vectors u=u(:) d=d(:) %LMS for n=M:N uvec=u(n:-1:n-M+1) e(n)=d(n)-w’*uvec w=w+mu*uvec*conj(e(n)) end e=e(:) Which value of µ results in quicker convergence? Which value of µ results in a smaller value for Jex (∞)? If you have time, simulate the case µ = 0.0075 for N = 2500 samples, and give an estimate for Jex (∞)! Compare your results with the results obtained by applying the rules of thumb for M. P.Radhika, Monpur Ashwin, Chunduri.V.M.Naren Simha. Give an estimate for Jex (∞) in Haykin, edition 4, figure 5.23, (edition 3: figure 9.23) for µ = 0.075 and µ = 0.025. Performance Analysis of Different LMS Algorithms for Health Monitoring ECG Sensor. The autocorrelation matrix can be generated in Matlab by R=sigmax2*toeplitz() +sigmav2*eye(11) Calculate the Wiener filter for W = 3.1, and determine Jmin. Computer exercise 2: Least Mean Square (LMS) This computer exercise deals with the LMS algorithm, which is derived from the method of steepest descent by replacing R = E for the system in Haykin yields   r(0) r(1) r(2).

Lms algorithm pdf