” 写作ECE 9203编程、 辅导MATLAB程序ECE 9203/9023 Random Signals, Adaptive and Kalman FilteringWinter 2021, MATLAB Assignment #1Due date time: Friday, February 19, 2021, 11 PM EDT.Upload to Assignments section. Email or DropBox submissions not accepted.1. (10 marks) Generate the following random signals in MATLAB. Plot the estimated probability densityfunction (PDF) and Power spectral density (PSD) for each. Comment on how close the estimated PDF andPSD are to their theoretical values. (see wgn.mlx for guidance).a. White Gaussian Noise, mean = 0, variance = 1b. White Uniform Noise, mean = 0, variance = 1c. Pink Gaussian Noise, mean = 0, variance = 12. (10 marks) In this exercise, we will apply AR modeling to speech samples. Download m01ae.wav,w01ae.wav, w01ih.wav, and w01uw.wav from Resources – MATLAB directory. Complete thefollowing:a. For each speech sample, plot the estimated variance of the white noise input against the model order,with the model order ranging from 1 to 25. See the documentation for aryule command foraccessing the estimated Variance. Comment on the results. What would be a good model order formodelling these waveforms?b. For each speech sample and the chosen model order, compute and plot the periodogram and ARspectral estimates. See LinearPredictionExample.mlx for guidance. Comment on the results. Inparticular, what is the AR spectral estimate trying to model? Are the AR spectral estimates the sameacross the four speech samples?3. (5 marks) The input to a Wiener filter of length two is described by the difference equation, u(n) = x(n) +v2(n), where x(n) = 0.3x(n-1) + 0.64 x(n-2) + v1(n), and v1(n) and v2(n) are zero-mean white noise processes ofvariances 0.4 and 0.2 respectively. The desired input is given by the difference equation, d(n) = 0.1x(n) +0.52 x(n-1). We derived the equations for the error performance surface and the Wiener filter for thisexample in class. Do the Following in MATLAB (see WienerFilterExample1.m for guidance):a. Plot the error performance surface as function of the weights.b. Plot the contours of the error performance surface and indicate the Wiener solution on this plot.c. Plot the gradient vectors and comment on their orientation.4. (15 marks) Consider a one-step adaptive predictor for a generic second order real AR process defined by thedifference equation u(n) + a1 u(n-1) +a2 u(n-2) = v(n), where v(n) is a zero-mean white noise process withvariance,!.a. Derive the equations for r(0), r(1), and r(2).=1, compute the eigenvalues, eigenvectors, and the eigenvalue spread. Using the LMSalgorithm with the convergence parameter, = 0.003, plot the power spectral densities for e(n). Include these plots in your assignment, clearly labeling the axes. What observationscan you make from These plots?d. Compute the ensemble-average learning curve of the LMS process by averaging the squared values ofthe prediction error, e(n). Similarly, compute the ensemble-average learning curves for the NLMSalgorithm using d = 0.05. Include these plots with your assignment, along with your observationscomparing the NLMS and LMS Results.如有需要，请加QQ：99515681 或WX：codehelp
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