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Unformatted text preview: ECE161A April 29, 2010 Discrete Time Signal Processing Professor T. Javidi Problem Sets #5 Due: May 6, 2010 1. Given a system with impulse response h [ n ] = ∞ X k =-∞ 2 δ [ n- 8 k ] + p (2) δ [ n- 1- 8 k ]- p (2) δ [ n- 3- 8 k ]- 2 δ [ n- 4- 8 k ]- p (2) δ [ n- 5- 8 k ] + p (2) δ [ n- 7- 8 k ] . (a) Find H (Ω) , the DTFT of h [ n ] . (b) Find the phase of H (Ω) . 2. Given x [ n ] = 2 δ [ n ] + 16 δ [ n- 1] + 16 δ [ n- 2] , and period N = 4 . find X (Ω) ,X (Ω) (the DTFT of the periodic version of x [ n ] ). Also find the 4 point DFT of x [ n ] . 3. Consider a function x [ n ] = 1 if n = 0 or n = 2 otherwise a. Take the 2-point, 3-point, and 4-point DFT of the signal, called X 2 [ k ] , X 3 [ k ] , and X 4 [ k ] . b. Take the inverse DFT of each (you can use MATLAB) and compare. Interpret the result. 4. Use the notes from discussion section to solve the following problem. You can also refer to the Matlab CD that accompanies the textbook. Also use Matlab help to learn about any new Matlab functionaccompanies the textbook....
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This note was uploaded on 09/10/2010 for the course ECE 107 taught by Professor Fullterton during the Spring '07 term at UCSD.
- Spring '07
- Signal Processing