20111ee102_1_homework5

20111ee102_1_homework5 - f ( t ) be a periodic function of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
is applied to it. 3. Let
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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

Page1 / 2

20111ee102_1_homework5 - f ( t ) be a periodic function of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online