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each for MUSIC and ESPRIT implementations, 10 pts for comparisons and discussions) Comparison of MUSIC and ESPRIT using MATLAB. (a) In MATLAB,...
each for MUSIC and ESPRIT implementations, 10 pts for comparisons and discussions) Comparison of MUSIC and ESPRIT using MATLAB. (a) In MATLAB, retrieve your signal set using command: filename = ['signalset' num2str(nstu) '_' num2str(ndam)]; load(filename); 'nstu' is your designated student number, 'ndam' is a flag indicating whether you are using the signal set that contains a damped (ndam=1) signal or an undamped (ndam=0) one. In the signal set, vector 'v' is the complex-valued sampled voltage sequence, and 'fs' is the sampling frequency. Then, analyze the frequency mode of the voltage sequence 'v' using MUSIC and ESPRIT. Please name your program hw4.m and start your MATLAB code with function hw4(nstu,ndam) [HINT: You should work with both the damped case and the undamped one. Each data set also contains a vector 'fr,' you should NOT need use that for this assignment. Please also use the complex magnitude estimation method instead of the absolute value one. You can also use K = 7 directly without having to estimate the number of modes in both methods.] (b) You can directly obtain the signal magnitudes |Ak|, initial phases φk, frequencies ωk, and the damping factor βk (ESPRIT only) for each of the K frequency modes. From the estimated |Ak|, φk, ωk, and βk values, describe how you can obtain the corresponding states x[n]. Then implement this in MATLAB. [HINT: For MUSIC, you can assume that βk = 0, ∀k.] Besides the algorithm development and the MATLAB code, your output should also contain the following five parts:The estimated frequencies, magnitudes, initial phases (in degrees) and damping factors (for ESPRIT). For grading convenience, please kindly keep these results in this exact order :-) ii) The mean square error (MSE) of the reconstructed signal to the reference of the given signal: N −1 PN n=1 |v[n] − vˆ[n]| 2 where N is the total number of samples in 'v'. An example for i) and ii) is given in Fig. 1. iii) In a single figure, but in separate subplots, plot the absolute values of each state versus time for MUSIC and ESPRIT. Since there is not much space for you to add legends for these curves, please follow the exact line color and style as the example in Fig. 2. Please DO also include xlabel and label as in the example. iv) In another figure, plot the real values of the last 20% samples of the given v[n] together with those of the reconstructed signals using MUSIC and ESPRIT. Please make sure that your curves are clearly identifiable and include legend, xlable and ylable. An example is shown in Fig. 3. [NOTE: You should clearly annotate all your outputs in terms of either the damped or undamped signal is considered.] v) Comparisons and discussions of results. Please do NOT include too many outputs in your submission. Use your judgement and pick only the representative ones and provide in-depth discussions on them. [NOTE: Your submission should contain one (1) hw4.m file and one (1) *.pdf or *.doc file collecting all your analysis, results and discussions.]
