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PS4-2010

PS4-2010 - filter(b Consider the above filter when k 1...

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ECE161A April 21, 2010 Discrete Time Signal Processing Professor T. Javidi Problem Set #4 Due: April 29th, 2010 1. Consider a causal filter whose output-input relation is k 1 y [ n ] + 3 y [ n - 2] = k 2 x [ n ] + k 3 x [ n - 1] - x [ n - 2] . (a) Pick a set of values for k 1 , k 2 , and k 3 to ensure that the output to the signal x [ n ] = cos(Ω n ) is a signal with amplitude 1, for all Ω [This is called an all pass
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Unformatted text preview: filter]. (b) Consider the above filter when k 1 =-3 , k 2 =-1 , and k 3 = 0 . Find its magnitude and phase response. Furthermore, calculate the output of the system when the input is cos[ πn 4 ] + cos[ πn 2 ] . 2. Problem 3.15 3. Problem 3. 23 4. Problem 7.15 5. Problem 7.21 Bonus Problem 3.11...
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