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HW7 (S 2007) - ELCT 321 Digital Signal Processing Homework...

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ELCT 321 Digital Signal Processing Homework Assignment # 7 (Frequency Response of FIR/ IIR Filters) by Dr. Yong-June Shin Assigned: April 12, 2007 Due: April 26, 2007 1. (20 Points) Consider a liner time-invariant system has frequency re- sponse H ω ) = (1 + e - j ˆ ω )(1 - e jπ/ 2 e - j ˆ ω )(1 - e - jπ/ 2 e - j ˆ ω ) The input ti the system is x [ n ] = 1 + 10 cos( π 2 n - π 4 ) + 5 δ [ n - 2] Use superposition to determine the corresponding output of the LTI system y [ n ]. 2. (20 Points) Suppose that S is a linear time-invariant system whose exact form is unknown. It is to be tested by observing the output signals corresponding to several different test inputs. Suppose that the following input-output pairs are the result of the tests: x [ n ] = δ [ n ] 7-→ y [ n ] = δ [ n ] - δ [ n - 3] x [ n ] = cos(2 πn/ 3) 7-→ y [ n ] = 0 x [ n ] = cos( πn/ 3 + π/ 2) 7-→ y [ n ] = 2 cos( πn/ 3 + π/ 2) (a) Determine the output when the input is x [ n ] = 2 δ [ n - 2] (b) Determine the output when the input is x [ n ] = 10 cos( π ( n - 3) / 3) (c) Determine the output when the input is x [ n ] = 10 cos(2 π ( n - 3) / 3)
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