18Summer_hw09.pdf

# 18Summer_hw09.pdf - University of Illinois Summer 2018...

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University of Illinois Summer 2018 ECE210 / ECE211 - Homework 09 Due: Thursday, July 19, 2018 @ beginning of class 1. Let f ( t ) = rect ( t - 1 2 ) , and h ( t ) given as, and let y ( t ) = f ( t ) * h ( t ) (a) Determine the value of t I , the first instant in time when y ( t ) is non-zero. (b) Determine the value of t F , the last instant in time when y ( t ) is non-zero. (c) Determine the values of y (0) , y (1) , y (2) and y (3) . 2. Let f ( t ) = 3 u (2 + t ) and h ( t ) = e - 2 t u ( t ) , and let y ( t ) = f ( t ) * h ( t ) . Determine y ( t ) for all -∞ < t < . 3. For the functions f ( t ) and g ( t ) sketched as shown below: (a) Determine x ( t ) = g ( t ) * g ( t ) by direct integration and sketch the results. (b) Determine y ( t ) = f ( t ) * g ( t ) using appropriate properties of convolution and the result of part (a). Sketch the result. (c) Determine z ( t ) = f ( t ) * f ( t + 2) using appropriate properties of convolution. Sketch the result. 4. Given h ( t ) = u ( t ) and f ( t ) = 3 4 ( t + 2) (a) Determine y ( t ) = h ( t ) * f ( t ) and sketch the result. (b) Determine z ( t ) = h ( t ) * df dt using appropriate properties of convolution, and sketch the result.
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