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Unformatted text preview: EE 4541 Digital Signal Processing Fall 2007 Problem Set Solutions 1. Problem 2.15 P&M. Note the typo: n=M a N n =L 6 points EE 4541 Digital Signal Processing Fall 2007 Problem Set Solutions 2. Problem 2.32 P&M
35 points 3. Problem 2.38 P&M. 6 points 4. Equations 2.5.21 and 2.5.22 are two equivalent implementations of the MA filter of order M. 6 points Compare the computational cost of these equations in terms of: a. Number of operations (e.g. additions, multiplications) per output sample. EE 4541 Digital Signal Processing Fall 2007 Problem Set Solutions b. Storage requirements. 5. Problem 2.52 P & M
35 points EE 4541 Digital Signal Processing Fall 2007 Problem Set Solutions 6. Use MATLAB's xcorr to verify the results of Example 2.6.1. Note that vectors in MATLAB represent causal sequences. It is the user's job to reinterpret the sample index values from the 6 points definition of n = 0 for x[n] and y[n]. The results of Problem 2.32 may be helpful. 7. Load the data from Assignment1.mat to your MATLAB workspace. Remove the DC 6 points component from each of the three waveforms (e.g. ecg1=deternd(ecg)) . The detrend command does more than just remove the DC, but its effect on the waveforms given will be limited to DC removal. Use xcorr to evaluate the cross correlation sequences for (work with the detrended waveforms): a. The aortic pressure waveform and the ECG waveform. For example, use the command xc1=xcorr(aortic1,ecg1,'coef'). The option `coef' produces a normalized correlation sequence. Define a lag vector l=-1999:1999; and plot the resulting sequence, e.g. plot(l,xc1). Identify the lag at which the sequence maximum value occurs. b. The aortic pressure waveform and the radial pressure waveform. Same as Part a. c. The aortic pressure waveform as an input to the MA filter (with M = 14) and the output. Plot this together with the autocorrelation sequence for the aortic pressure (This can be obtained using xcorr.) Where does the maximum value occur for each sequence? Comment on your result. d. The aortic pressure waveform as an input to the MA filter (with M = 8) and the output. Same as Part c. Compare the results with the results in Part c. e. Can you explain the relationship between the aortic and radial pressure waveforms based on the results of Part c. and d? ...
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