sol4 - ECE 351, Systems I OSU, Winter 2009 Solutions -...

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ECE 351, Systems I Feb. 23, 2009 OSU, Winter 2009 Solutions - Problem Set 4 Problem 1 (a) FALSE. The system is BIBO stable for all | a | < 1. Thus it is unstable for a > 1. (b) TRUE by de±nition of causality. (c) FALSE. One cannot write the impulse response in the form h [ n ] = [ n ] for the given values of a and b . (d) TRUE. Here x 2 ( t ) is a pulse with a span between (0 , 1). If x 1 ( t ) is ²ipped and shifted by 1, the area under it between 0 and 1 is 0. (e) FALSE. If x 1 ( t ) is ²ipped and shifted by 2, there remains no overlap with x 2 ( t ). Thus the convolution at t = 2 is 0. (f) FALSE. If x 1 ( t ) is ²ipped and shifted by 1 / 2, the overlap with x 2 ( t ) is between 0 and 1 / 2. The area of the corresponding triangular region is 1 / 4. (g) FALSE. An LTI system cannot give a non-zero response at a frequency, not induced by the input. (h) FALSE. x ( t ) is periodic with a period T = 1 250 = 4 msec.
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sol4 - ECE 351, Systems I OSU, Winter 2009 Solutions -...

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