# hw3 - EE210 Signal Systems (January 29, 2009) Home Work Set...

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EE210 Signal Systems (January 29, 2009) Home Work Set 3 1. For the circuit shown ﬁnd atleast two distinct state variable representation, ﬁnd the relation between them. Figure 1: For problem no. 1 2. Show that e ( A 1 + A 2 ) t = e A 1 t .e A 2 t if A 1 A 2 = A 2 A 1 3. Let h ( t ) be the triangular pulse shown below and input x ( t ) (a sequence of δ fucntions) as shown. Determine and sketch y ( t )= x ( t ) * h ( t ) for (i) T=4 (ii) T=1.5 Figure 2: For problem no. 3 4. Let x 1 ( t ) and x 2 ( t ) be two periodic signals with period T. The periodic convolution between x 1 ( . ) and x 2 ( . ) is deﬁned as y ( t ) = Z T 0 x 1 ( t ) x 2 ( t - τ ) = x 1 ( t ) x 2 ( t ) (a) Show that y ( t ) is periodic with period T (b) Let y α ( t ) =

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## This note was uploaded on 02/01/2012 for the course EE 210 taught by Professor Prof.h.narayanan during the Spring '07 term at IIT Bombay.

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hw3 - EE210 Signal Systems (January 29, 2009) Home Work Set...

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