HW2 - First use stationary random data Then use...

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HOMEWORK #2 1. In the Matlab script “ensemble_vs_time_avg.m” discussed in class, is the ensemble average technique using the sampling rate ( 1 8192 sec. dt = ) and number of samples in each block (8192) always effective in eliminating the random noise component in the signal, regardless of the frequency and initial phase angle of the sine component at time t=0? In particular, what is the requirement for the sinusoid frequency for the ensemble average denoising scheme to work? Can you generalize this result by making a statement about the requirement on the number of cycles in each sample block? (2 points) 2. Write a Matlab function to perform the reverse arrangement test. The function should take as input a random variable (i.e., a vector x ) and split it into a user defined number of sample records, Nrec , of equal length and return the total # of reversals of the mean-square value of each record. Validate your code using the data in Ex. 4.4. Then use real data (or Matlab-generated data) to test your code.
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Unformatted text preview: First, use stationary random data. Then, use nonstationary data. Include the code, plots of the data, etc. in your results. Explain your results. (2 points) 3. B&P 1.6 (1.3 in 3 rd edition) (1 point) 4. B&P 1.7 (1.4 in 3 rd edition) (1 point) 5. B&P 1.8 (1.5 in 3 rd edition) (1 point) 6. B&P 1.4 (1.9 in 3 rd edition) (1 point) 7. B&P 1.5 (1.10 in 3 rd edition) (1 point) 8. Write (type) a brief summary concerning your plan for a term paper. You may write about a topic that concerns this course (data measurement & analysis). It can be about application of the methods and (hopefully) some extension to new methods or analysis. If you don’t have a topic in mind, consider the following possibilities: beamforming, time-frequency analysis, Proper Orthogonal Decomposition, Kalman filtering, linear stochastic estimation, wavelets, higher-order spectral analysis, etc. For these, you could write a tutorial paper about the theory and provide some numerical Matlab examples. (1 point)...
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