5. (5 points) Consider the continuous-time signal x(t) given by the following expression, where the con-stants a, b, c are greater than zero (a > 0, b > 0, c> 0), and a b, asx(t)ceatt<0,t≥0."Determine the Fourier Transform X(jw) of x(t) using the definition.

Answered: 5. (5 points) Consider the…

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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1. Write down the definition of a 1-D Fourier transform. Use this definition to find the Fourier Transform of a rectangular function of arbitrary width W. What happens as (1) W→∞ and (2) as W→0? Include a sketch of the result. rect(X/W) -W/2 W/2
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
2. A function f(t) has Fourier transform, F(w) = we-w². What are the Fourier transforms of: (a) f(t-3) (b) f(1/2) (c) f(¹=³)
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Hi, the attached image shows a question and its answer but still, I couldn't understand it please simply explain it
4. A. Find the Fourier Transform of the signals below. a. x(t) = sinc²(t).cos(6mt). (Find by plotting) b. x(t) = e-t+2.u(t-2). c. x(t) = t.e-3ltl B. An LTI system has the input-output differential equation given by d² y(t) dy(t) +45 -+3y(t) = 2x(t) dt² dt a. Find its frequency response. b. Find its impulse response.
Suppose that X(w) is real but not even. Can we conclude whether X[n]must be or cannot be real ? Can we conclude whether X[n]must be or cannot be even ? Remark: There is one wrong answer that will still give you +1 point. Hint 1: This is based on the logical use of several properties of Fourier transform. Hint 2: If a" = a, what do you conclude ? Hint 3: If a sequence y[n] is Hermitian symmetric, is it true or not that y[n] is real if and only if y[n] is even ? X[n]must be real, and we cannot conclude on its even symmetry. nX[n]cannot be real, and we cannot conclude on its even symmetry. Oxn]must be even, and we cannot conclude whether it is real or not. Oxn]cannot be even, and we cannot conclude whether it is real or not. OXIN]must be real and must be even. xn]must be real and cannot be even. Xn)cannot be real and must be even. x(n]cannot be real and cannot be even. None of the above.
Signal and systems question help me pls thanks
A Fourier transform M(jw) is shown below: -ZT(100) 2πT(100) Determine the corresponding time signal m(t). Hint: can you write M(jw) as the convolution of two other Fourier transforms? Does this help to find the inverse?
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
The following are the Fourier transforms of discrete-time signals. Determine the signal corresponding to each transform. (a) X(e) = 1 + 3e-jw - 5e4jw (b) X(ejw) = 3e-jw _1 4-e-jw

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5. (5 points) Consider the continuous-time signal x(t) given by the following expression, where the con- stants a, b, c are greater than zero (a > 0, b > 0, c> 0), and a b, as x(t) ceat t<0, t≥0. " Determine the Fourier Transform X(jw) of x(t) using the definition.