102_1_MidtermSpring2008Solution

102_1_MidtermSpring2008Solution - HW6 solution, SPRING...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
HW6 solution, SPRING 2008, EE 102 1. (i)It’s Linear, and Causal. (TI or TV?) Let x ( t ) = δ ( t - τ ) y ( t ) = 1 t + 1 U ( t - τ ) It’s TV. (ii) y ( t ) = 1 t + 1 Z t 0 U ( σ - 1) = 1 t + 1 U ( t - 1)( t - 1) (iii) y ( t ) = 1 t + 1 Z t 0 δ ( σ - 2) = 1 t + 1 U ( t - 2) . 2. y ( t ) = [ e - t U ( t )] * x ( t ), Thus, h 1 ( t ) = e - t U ( t ) For S 2 , h 2 ( t ) = δ ( t ) - U ( t ). h 21 ( t ) = Z -∞ h 1 ( t - σ ) h 2 ( σ ) = [2 e - t - 1] U ( t ) . (ii) BT: y ( t ) = Z -∞ h ( t,τ ) x ( τ ) For TI system, h ( t,τ ) = h ( t - τ ) For the property given in the question: y ( t ) = Z -∞ h ( t - τ ) x ( τ ) = Z 0 -∞ h ( t - τ ) x ( τ ) + Z 1 h ( t - τ ) x ( τ ) 3. (i) Original formula= ee t - 1 δ ( t - 1) + e - 1 e - ( t - 1) U ( t - 1) e - s [ e + e - 1 1 s +1 ] (ii) 1 2 [ 1 s +2 + cos 2 π 3 ( s +2 ( s +2) 2 +4 ) + sin 2 π 3 1 ( s +2) 2 +4 ] 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
4. (i)
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

102_1_MidtermSpring2008Solution - HW6 solution, SPRING...

This preview shows document pages 1 - 3. Sign up to view the full document.

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