soln5 - ECE320 Solution Notes 5 Cornell University Spring...

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ECE320 Solution Notes 5 Spring 2006 Cornell University T.L.Fine 1. For each of the systems of Sections 5.2.1 through 5.2.5 provide a repre- sentation of the form of Section 5.2.9 by defining h ( t, τ ), if possible, and explain if it is not possible. 5.2.1 of a fixed output system is not a linear system (summing two signals f 1 , f 2 does yields output g o and not 2 g 0 . Hence, it does not have the impulse response representation. 5.2.2 of time selection is a linear system and the result is achieved by the impulse response function h ( t, τ ) = δ ( τ - t o ). 5.2.3 of memoryless is a linear system only if the function h ( f ) = af . In that case the impulse response function h ( t, τ ) = ( t - τ ). If h is not a linear function then the system is nonlinear and cannot have an impulse response representation. 5.2.4 of delay by D o is linear and is obtained from the impulse response function h ( t, τ ) = δ ( t - D o - τ ). 5.2.5 of amplification by α o is a linear system and use h ( t, τ ) = α o δ ( t - τ ). 2. (a) Provide an example of a homogeneous system that is not representable by an impulse response system. Such an example is given in 5.2.6.
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