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Unformatted text preview: NAME: 31 Oct. 2011 ECE 538 Digital Signal Processing I Exam 2 Fall 2011 Cover Sheet WRITE YOUR NAME ON THIS COVER SHEET Test Duration: 60 minutes. Open Book but Closed Notes. Calculators NOT allowed. All work should be done in the space provided. 1 EE538 Digital Signal Processing I Exam 2 Fall 2011 Problem 1. Consider four different signals with the spectral shapes shown in Figure 1 on the next page, each of which is sampled at the Nyquist rate. Digital subbanding of the the DT signals is effected via the system in the block diagram in Figure 1. The respective impulse responses for the four filters f k [ n ] = e j ( k 2 π 4 ) n h LP [ n ] , k = 0 , 1 , 2 , 3 are defined in terms of the ideal lowpass filter below h LP [ n ] = 4 sin( π 4 n ) πn . (1) (a) Plot the magnitude of the DTFT Y ( ω ) of the final sum output y [ n ] over- π < ω < π . You will lose credit if you just do the plot with no supporting work and/or explanation. At the same time, though, be concise and don’t overdo it as you have to save time for the other parts of this exam. Note that 6 π 4 = 3 π 2 is the same DT frequency as- 2 π 4 =- π 2 ....
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