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20111ee102_1_homework5

# 20111ee102_1_homework5 - f t be a periodic function of...

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WINTER 2011: Put Discussion section number in the corner →→→ (* Otherwise Your HW will be LOST) Name(Print) (LAST, Middle, First): ————————————— Student ID : ——————————————————– HW: # 5 NO LATE HOMEWORK POLICY! Posted: February 4 Hand In: February 11 at (Eng IV 56-125B) Attach This Sheet To Your HW 1. Realize the signal y ( t ) = ( - 7 e 3 t + 8 e 4 t ) U ( t ) as the output of a L, TI, C system S when an appropriate input x ( t ) is applied to S . Write down the IRF h ( t ) of S and the input x ( t ). x ( t ) =? [ L, TI, C, h ( t ) =?] y ( t ) = ( - 7 e 3 t + 8 e 4 t ) U ( t ) . 2. Consider the cascaded systems: x ( t ) S 1 z ( t ) S 2 y ( t ) where S 1 and S 2 are L, TI, C. Moreover, S 1 is described by the IPOP relation z ( t ) = i t 0 e ( t τ ) x ( τ ) dτ, while the Unit Step Response g 2 ( t ) of S 2 is g 2 ( t ) = te t U ( t ). Your problem is to compute the output y ( t ) of the cascaded combination S 12 = S 1 S 2 when the input x ( t ) = δ ( t ) + 2 cos tU ( t ) 1

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is applied to it. 3. Let
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Unformatted text preview: f ( t ) be a periodic function of period T . Show that F ( s ) = 1 1-e − sT i T e − st f ( t ) dt. Use this result to compute the Laplace transforms of the functions presented in question 3.4 in the textbook (page 69). 4. Find the system function and the impulse response function of the system whose input x ( t ) and output y ( t ) are related by d 2 y dt 2 + 3 dy dt + 2 y ( t ) = 2 dx dt + x ( t ) , y (0) = y ′ (0) = x (0) = 0 . 5. Let F ( s ) denote the Laplace transform of f ( t ). Given F ( s ) = 2 s s 3 + 2 s 2 + 2 s + 1 . (i) Find f ( t ). (ii) Express f ( t ) as a convolution integral. If the function f ( t ) found in (i) is the output of an LTI and causal system S when e − t U ( t ) is applied to it, ±nd the impulse response function h ( t ) of S . 2...
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20111ee102_1_homework5 - f t be a periodic function of...

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