HW4 - ELEN3801 Fall 2009 Homework 4 Due Thursday October...

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

ELEN3801 - Fall 2009 Homework 4 Due Thursday October 8th at the beginning of class (Mudd 227 9:10am) 1 Carefully justify ALL your answers 4.1 - Let H be a time-invariant (but not necessarily linear) system. Show that the system’s response to a constant input is also a constant, that is, if the input is f ( t ) = a for all t R , then H { f ( t ) } = b , where b R . 4.2 - Consider an LTI system that has impulse response h ( t ) = e - t u ( t ). Find the system response y ( t ) if the input is (a) u ( t ) (b) e - t u ( t ) (c) sin(3 t ) u ( t ) 4.3 - (CORRECTED) Let p ( t ) = u ( t + 1) - u ( t - 1). Compute and sketch ( p * p )( t ) and ( p * p * p )( t ). Comment on your results. 4.4 - Consider a system that has impulse response h ( t ) = - δ ( t ) + 2 e - t u ( t ). Compute the system’s response to input e t u ( - t ) and sketch both the input and output signals. 4.5 - (Optional) Prove the associativity property of the convolution. That is, prove that ( f 1 * ( f 2 * f 3 )) ( t ) = (( f

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/08/2011 for the course EE 111 taught by Professor Kim during the Spring '11 term at Korea University.

Page1 / 2

HW4 - ELEN3801 Fall 2009 Homework 4 Due Thursday October...

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

View Full Document
Ask a homework question - tutors are online