20111ee102_1_discussion2

# 20111ee102_1_discussion2 - WINTER 2011 EE102 SYSTEMS...

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WINTER 2011: Discussion: # 2 Posted: January 14 1. (i) Write down the IRF h ( t,τ ) of the following system: y ( t ) = Z -∞ e - t ( t - τ ) U ( τ - t ) x ( τ ) dτ, t ( -∞ , ) . (ii) Given the IRF h ( t,τ ) of a L, TI, C system: h ( t,τ ) = e - ( t - τ ) ( t - τ ) U ( t - τ ) , for t,τ ( -∞ , ) . and the input x ( t ) = δ ( t - 2) - e - t U ( t ) , t ( -∞ , ) . Find the corresponding output y ( t ). (iii) A system S whose IPOP relation is b ( t ) = Z t -∞ ( t - σ ) a ( σ ) dσ, where a ( · ) and b ( · ) denote input and output, respectively. Find the IRF h ( t,τ ) of S , and ﬁnd its response due the input U ( t ) — called the step response , denoted by g ( t ). 2. Given that a system

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## This note was uploaded on 10/07/2011 for the course EE 102 taught by Professor Levan during the Spring '08 term at UCLA.

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20111ee102_1_discussion2 - WINTER 2011 EE102 SYSTEMS...

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