ECE108Exam%231sol_06

# ECE108Exam%231sol_06 - Name ECE 108 Exam#1 1 Given 30pts 1...

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____________________________________________ Name ECE 108 Exam#1 2/17/06 1. Given 30pts () 2 1 2 n yn xn  =   Justify the answer to the following two questions (a) Is the system time-invariant? 22 2 0 00 11 1 2 nn Txn Txnn xnn yn n xn n  = −=  Therefore ( ) ( ) T xn n −≠ THE SYSTEM IS TIME-VARYING (b) Is the system linear? () () 2 2 12 1 2 1 2 1 2 n n Tx n x n x n x n x n x n αβ α β = + = + = + = + THE SYSTEM IS LINEAR

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2 2. Given an input and the impulse response of a LTI system as shown below 35pts Use convolution to determine y ( t ), i.e., () ( ) ( ) yt x ht d τ ττ −∞ =− To carry out this convolution, the integral must be partitioned into different intervals (Cases). For Case 1 (t < 0) and Case 6 (t > 8) it is obvious that y ( t ) = 0. For each of the remaining Cases provide the following information * The range of values of t over which it is valid * The integration required to determine y ( t ). Make sure you include the limits of integration and the appropriate mathematical expression in the integrand.
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ECE108Exam%231sol_06 - Name ECE 108 Exam#1 1 Given 30pts 1...

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