Please answer in typing format Lets define:x1(t) → X1(S) & x2(t) → X2(S)Show that:8L x1(t)x2(t)dt = √ X₁(S) X2(–S)ds-∞Tip: Use the convolution property2πT -∞

Step 1:The convolution property of Fourier transforms;Explanation:The convolution property states…

Answered: Lets define: x1(t) → X1(S) & x2(t) →…

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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Similar questions

Calculate y(t)=x(t)*v(t) using the convolution integral for the continuous signals x(t) and v(t) given in the figure below. Write the result of y(t) as a piecewise function. Also, show the result in an approximate way by drawing a graph.
For the circuit in the figure, determine the response of i(t), valid for all t=0- and t=0 , if at t=0+, the switch opens.note: solve the edo without laplace
The switch in the circuit has been closed for a long time before opening at t=0. 1. a) Construct the s-domain equivalent circuit for t>0. 2. b) Find Io. 3. c) Find io for t≥0.
The signal is given by: f(t) = 0⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ if ⁡t < 0 f(t) = 1 − t/3 ⁡⁡⁡if ⁡0 ≤ t ≤ ⁡⁡3 f(t) = 0⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ if⁡ t > 3 (i) Give the graphical representations of the signals (f). (ii) Give a physical meaning of the convolution product of two signals. We set h(t) = f(t) *f(t) where '*' represents the convolution product. (iii) Determine the signal (h).
The switch in the circuit shown has been in position a for a long time. At t=0, the switch moves instantaneously to position b. 1. Derive the integrodifferential equation that governs the behavior of the current io for t≥0+. 2. Show that Io(s)=Idc[s+(1/RC)][s2+(1/RC)s+(1/LC)].
The step response of an continuous-time LTI system is given by (1 - e-t)u(t). For a certain unknown input x(t) , the output y(t) is observed to be (2 - 3e-t + e-3t)u(t). a) Find the input x(t) as a function of time. b) Is this system BIBO stable.
The circuit shown below has been in that situation for a long time. At t=0, part of the circuit is cut down from the dashed line. Determine vC1(t) for t > 0.
Circuit analysis 2 In the circuit shown below, the value of ic (t) for t <0 is equal to which of the following?
A continuous-time LTI system is described by d^2y(t)/dt^2 + 4[dy(t)/dt] + 3y(t) = 2dx(t)/dt + 4x(t). Assuming zero initial condition, find out the response y(t) of the above system for the input x(t) = e^(−2t)u(t).
The step response of an continuous-time LTI system is given by (1 - e-t)u(t). For a certain unknown input x(t) , the output y(t) is observed to be (2 - 3e-t + e-3t)u(t). a) Find the input x(t) as a function of time. b) Is this system BIB0 stable.
A causal linear time-invariant continuous-time system has impulse response h(t) = e-t +sin(t) , t >= 0 Compute the output response for all t>=0 when the input is the unit-step function u(t).
Signal and system The mathematical model of a system is y" (t) + ay'(t) + by(t) = a (t) + ca (t) where a=1, b=2 and c=1. 1) Find zeros and poles of the system. 2) Show them onto the S-Plane (the complex plane) 3) Discuss the BIBO stability of the system.

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Lets define: x1(t) → X1(S) & x2(t) → X2(S) Show that: 8 L x1(t)x2(t)dt = √ X₁(S) X2(–S)ds -∞ Tip: Use the convolution property 2πT -∞