ECE2101_HW7SOL_SpS19.pdf - Spring Semester 2019 ECE 209 — Network Analysis II A Gonzalez California State Polytechnic University Pomona Department of

# ECE2101_HW7SOL_SpS19.pdf - Spring Semester 2019 ECE 209 —...

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Spring Semester 2019 ECE 209 — Network Analysis II A. Gonzalez California State Polytechnic University, Pomona Department of Electrical and Computer Engineering Homework 7 Solutions Due : Friday, May 10, 2019 by 11:59 PM. Additional notes : Graphical approach must be done by hand. 1. Using the graphical approach , find y ( t ) = x ( t ) * h ( t ) for each paired x ( t ) and h ( t ) in Figure 1 . x ( t ) t 0 1 1 h ( t ) t 0 1 1 (a) x ( t ) t 0 1 h ( t ) t 0 2 2 e - t (b) Figure 1: Signal pairs 1

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Spring Semester 2019 ECE 209 — Network Analysis II A. Gonzalez (a) Flip and slide x ( t ). For 0 < t < 1, x ( t - λ ) and h ( λ ) overlap as follows λ 0 t t - 1 1 1 x ( t - λ ) h ( λ ) y ( t ) = x ( t ) * h ( t ) = Z t 0 (1)( λ ) = t 2 2 For 1 < t < 2, x ( t - λ ) and h ( λ ) overlap as follows λ 0 t t - 1 1 1 y ( t ) = x ( t ) * h ( t ) = Z 1 t - 1 (1)( λ ) + Z t 1 (1)(1) = - 1 2 t 2 + 2 t - 1 For t > 2, there is complete overlap as follows λ 0 t t - 1 1 1 y ( t ) = x ( t ) * h ( t ) = Z t t - 1 (1)(1) = 1 Therefore, y ( t ) = t 2 2 0 < t < 1 - 1 2 t 2 + 2 t - 1 1 < t < 2 1 t > 2 0 otherwise 2
Spring Semester 2019 ECE 209 — Network Analysis II A. Gonzalez (b) Let’s flip and slide x ( t ). For t > 0 the two functions overlap as follows λ 2 h ( λ ) = 2 e - λ x ( t - λ ) 1 0 t y ( t ) = x ( t ) * h ( t ) = Z t 0 (1)(2 e - λ ) = 2(1 - e - t ) Therefore, y ( t ) = 2(1 - e - t ) , t > 0 3

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Spring Semester 2019 ECE 209 — Network Analysis II A. Gonzalez 2. Using the graphical approach , obtain the convolution of the pairs of signals in Figure 2 .
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• Academic term, Figure 8, 2T, G 3/08, A. Gonzalez

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