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12 The impulse response of an LTI is h(t) =r(t) – 2r(t – 1) +r(t – 2) and the input is a sequence of impulses x(t) = >8(t – kT). k=0 (a) Find the system output y(t) as the convolution integral of x(t) and h(t), and plot it for T = 1 and T =2. (b) For T = 2 obtain the Laplace transform Y (s) of y(t). Answer: Y (s) = (cosh(s) – 1)/(s² sinh(s)).

12 The impulse response of an LTI is h(t) =r(t) – 2r(t – 1) +r(t – 2) and the input is a sequence of impulses x(t) = >8(t – kT). k=0 (a) Find the system output y(t) as the convolution integral of x(t) and h(t), and plot it for T = 1 and T =2. (b) For T = 2 obtain the Laplace transform Y (s) of y(t). Answer: Y (s) = (cosh(s) – 1)/(s² sinh(s)).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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12 The impulse response of an LTI is h (t) =r(t) – 2r (t – 1) +r(t – 2) and the input is a sequence of impulses x() Σδ( - kT). k=0 (a) Find the system output y(t) as the convolution integral of x(t) and h(t), and plot it for T = 1 and T =2. (b) For T =2 obtain the Laplace transform Y (s) of y(t). Answer: Y (s) = (cosh(s) – 1)/(s² sinh(s)).
Transcribed Image Text:12 The impulse response of an LTI is h (t) =r(t) – 2r (t – 1) +r(t – 2) and the input is a sequence of impulses x() Σδ( - kT). k=0 (a) Find the system output y(t) as the convolution integral of x(t) and h(t), and plot it for T = 1 and T =2. (b) For T =2 obtain the Laplace transform Y (s) of y(t). Answer: Y (s) = (cosh(s) – 1)/(s² sinh(s)).
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