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# hw3 - ASE 330M Linear System Analysis Unique Number 12880...

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ASE 330M Linear System Analysis Unique Number: 12880, Spring 2007 Homework #3 Basics of Signals and Systems Date given: February 22, 2007 Date Due: March 6, 2007 1. The systems given below have input x ( t ) and output y ( t ) respectively. Determine whether each of them is: (i) causal, (ii) linear, (iii) time invariant, and (iv) memoryless. Assume zero initial energy for the system in part (c). Make sure to provide elaborate justiﬁcations to your answers. (a) y ( t ) = cos( x ( t )) (b) y ( t ) = - x ( t ) + e - t - 1 (c) ˙ y ( t ) = ty ( t ) x ( t ) (d) y ( t ) = x (2 - t ) (e) y ( t ) = ( t + 3) x ( t - 2) (f) y ( t ) = R t -∞ ( t - τ ) x ( τ ) (g) y ( t ) = e - t ˙ x ( t ) (h) y ( t ) = x ( at ) for both cases a < 1 and a > 1. 2. A system initially at rest is speciﬁed by its input-output relationship as y ( t ) = x 2 ( t ) ˙ x ( t ) Discuss whether it is a linear system or not. 3. Consider a signal x ( t ) deﬁned as follows: x ( t ) = 0 , if | t |≥ 1 1 + t,

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hw3 - ASE 330M Linear System Analysis Unique Number 12880...

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