102_1_vdis3

102_1_vdis3 - EE102 Discussion 3 vasiliy karasev 1 LTI System Response impulse 1 impulse response(t 1*h(t 1 h(t = e-atu(t 1 0 complex input 1 t x(t

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

View Full Document Right Arrow Icon
EE102 Discussion 3 2010-10-11 vasiliy karasev 1. LTI System Response δ(t) t 1 0 1 h(t) = e u(t) -at t 1 0 1 *h(t) impulse impulse response x(t) t 1 0 1 *h(t) y(t) = ? t 1 0 1 complex input complex output Linearity allows representing x [ n ] as a sum of weighted δ functions: x [ n ] = ... + x [ - 1] δ [ n + 1] + x [0] δ [ n ] + x [1] δ [ n - 1] + ... Time Invariance asserts that output to delayed delta function is the delayed impulse response h ( t ). δ [ n ] 7→ h [ n ] δ [ n - 1] 7→ h [ n - 1] ... Linearity claims that weighted, delayed impulse responses can be summed to produce y [ n ]: y [ n ] = ... + x [ - 1] h [ n + 1] + x [0] h [ n ] + x [1] h [ n - 1] + ... This can also be summarized (in continuous time) as: x ( t ) = Z -∞ x ( τ ) δ ( t - τ ) y ( t ) = Z -∞ x ( τ ) h ( t - τ ) = ( x * h )( t ) = ( h * x )( t ) Exercise 1. f ( t ) = u ( t ), g ( t ) = δ ( t ) - δ ( t - 1). Find ( f * g )( t ).
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/20/2011 for the course EE 102 taught by Professor Levan during the Fall '08 term at UCLA.

Page1 / 3

102_1_vdis3 - EE102 Discussion 3 vasiliy karasev 1 LTI System Response impulse 1 impulse response(t 1*h(t 1 h(t = e-atu(t 1 0 complex input 1 t x(t

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