The output of a causal LTI system is related to the input x(t) by the differential equationdy(t) + 2y(t) = x(t)dt(a) Determine the frequency response H(@) = and sketch the phase and magnitude of H(w)(b) If x(t) = e tu(t), determine Y(@), the Fourier transform of the output.(c) Find y(t) for the input given in part (b).X(@)

Answered: The output of a causal LTI system is…

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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3) Consider the signal. Xo(-t) -1 Xo(t +1) -1 0 Using only the Fourier Transform of xo(t) and Fourier Transform properties, determine the Fourier Transform of each signal shown in the Figure below. x₁ (t) X₂(t) (a) X3(t) 0 (c) x (t) xo(t) 1 xo(t) 1 = t e 0, t " 0 ≤t≤1 elsewhere -1 -Xo(-t). (b) xo(t) (d) 1 X4(t) txo(t) La 0 1 t (1) t
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Using the definition of Fourier transform F(a)=f(t)e-ltdt The Fourier transform of f(t)- e*u(-t) F(w) is: Select one: O F(w)-0 O F(w)=-1/(2 + jw) O F(w)=1/(2+ jw) O F(w)=1/(2-jw)
h(t) 1 Q1: For the signal h(t), shown in figure beside. 1 i) Find Fourier Transform H(w) ii) Sketch amplitude and phase spectrum of H(w) -1
Question 3 Below is a Boolean expression. For the circuit corresponding to this Boolean expression, there is an equivalent circuit with at most two logic gates. Find it. Be sure to show your work. (~ P^~Q) V (~ PAQ) V (PA~Q)
For the following signals, x(t), use the Fourier Transform “Common Signals" Table and the "Properties" table to write the formula for the Fourier Transform, X(@). Where indicated, sketch by hand the Real Part of X(@) on one graph & the Imaginary Part of X(@) on a SEPARATE graph. ) x(t) = 4 rect1o(2t) +> X( @) = ??? Plot X(@)??? %3D
The periodic signal x(t) is shown in the following figure. It is a rectangular pulse repeated every 4 seconds. a) Write the mathematical representation of x(t) b) What is the Fourier Transform of x(t)? c) Sketch X(@), showing the important parameters. Make sure you show the magnitude of X(@) at w = 0.
1 Assume that z(t) and y(t) are both continuous time aperiodic signals, and Fourier transform z(t) is X(w). What is the Fourier transform of y(t) = r(t) – 2z(t – to)? Select one: a. Y(w) = X(w) - 2X(w+ 2un) b. Y(w) = X(w) c. Y(w) = X(w) – 2X(w)e juto O d. Y(w) = X(w) + 2X(w)eiutu
Ql: For the signal g(t), shown in figure beside. 10 i) Find Fourier Transform G(w) ii) Sketch amplitude and phase spectrum of G(w) -1
Periodic signal x(t) which is shown in

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