# Ps3 - x t to y 1 t in the circuit of Figure P1.8-1 in Lathi 4 For a certain LTI system the impulse response h t = e a t-t u t-t(a For what values

This preview shows page 1. Sign up to view the full content.

Michigan State University Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING Problem Set 3 Spring 2011 Issued: Friday, January 28, 2011 Due: Friday (8:00am), February 4, 2011 1. Problems 2.4-16 and 2.4-17 in Lathi (Use properties to solve the latter problem.) 2. Problem 2.4-18a in Lathi 3. In this problem, you will determine the impulse response of a circuit using time-domain techniques. (a) Show that the impulse response h ( t ) of an LTI system may be determined by diﬀerentiating its step response s ( t ) (i.e., the output of the system to the input u ( t )). (First, use δ ( t ) = du ( t ) dt . Then, use dx ( t ) dt = lim T 0 x ( t ) - x ( t - T ) T . Finally, invoke linearity and time-invariance.) (b) Use the above result to compute the impulse response relating
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ( t ) to y 1 ( t ) in the circuit of Figure P1.8-1 in Lathi. 4. For a certain LTI system, the impulse response h ( t ) = e a ( t-t ) u ( t-t ). (a) For what values of a and t is the system causal? (b) For what values of a and t is the system BIBO stable? (c) For what values of a and t is the system marginally stable? (d) Compute the output y ( t ) of the system with a =-1 and t = 0 in response to the input f ( t ) = e j (2 πt + π/ 4) . How are the input and output related? (e) Compute the output y ( t ) of the system with a =-1 and t = 0 in response to the input f ( t ) = cos(2 πt + π/ 4)). How are the input and output related?...
View Full Document

## This note was uploaded on 10/17/2011 for the course ECE 366 taught by Professor Staff during the Spring '08 term at Michigan State University.

Ask a homework question - tutors are online