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**Unformatted text preview: **EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions 1. Problem 10.1 P&M EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions 2. Problem 10.2 P&M EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions 3. Problem 10.9 P&M 4. Problem 10.22 a)&b) P&M EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions 5. Problem 10.31 P&M (Grad Students). EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions 6. MATLAB Problem: Pulseecho Ultrasonic Data a. Download the file Assignment11.mat from the Assignment11 folder and save it to your working directory. b. The file contains a matrix (named rfdat1) with 26 columns and 1500 rows. Each column is a sequence of samples acquired by an imaging transducer with sampling frequency of 33 MHz. In ultrasound imaging, these sequences are called Alines. c. Load the data to your workspace and use the plot and imagesc commands to visualize the data. For example: load Assignment11 plot([rfdat1(:,1) rfdat1(:,2) rfdat1(:,13)]) legend('A-line 1','A-line 2','A-line 13') xlabel('Sample Index'); ylabel('Amplitude') Displays Alines 1, 2, & 13 as follows: You can use imagesc as follows: imagesc(rfdat1); EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions xlabel('A-line Index'); ylabel('Sample Index') which displays an image of the data as follows: You can see that Alines 9 and 10 are different from the others. This is due to strong interference from a highpower transducer that was used to heat the tissue sample being interrogated. It is also possible that Alines 8 and 11 may have some interference. Please note that the 2D display is not a real image. It is just a visual representation of the data acquired at different times. d. For each of the Alines recorded in this data set: i. Determine the range of frequencies within 20 dB from the maximum. You will need to use the pwelch command for this. Give your answer in terms of the physical frequencies in MHz. You can use the default setting for pwelch, but give the window type, window size, and fft size used by this command. Describe the effect of the window function used on the observed spectral estimate. ii. Determine which lines have strong interference from the highpower source. Determine the fundamental and any harmonics that interfere with the spectrum. EE 4541 Digital Signal Processing Fall 2007 Problem Set 11 Solutions iii. Design an appropriate notch filter to remove the interference from the fundamental and any existing harmonics. Use MATLAB's zerophase implementation filtfilt only on the Alines that have interference. iv. For each of the lines that you filtered with your notch filter, plot the unfiltered and filtered waveforms and their spectra for comparison. v. Comment on the transient response of your filter(s). ...

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