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

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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
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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?...
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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.

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