Consider a signal sin (40πt) πt a) Find its Fourier transform defined by using regular frequency X(f) = a(t)e-1²f¹ dt = X(w) |w=2″ f x(t) = b) A sampled signal x, (t) is obtained using a sampling frequency f,= 50 samples/second. Please find and plot its Fourier transform X, (f). c) Can we reconstruct the signal r(t) from its samples or not? Please also explain why.

Consider a signal sin (40πt) πt a) Find its Fourier transform defined by using regular frequency X(f) = a(t)e-1²f¹ dt = X(w) |w=2″ f x(t) = b) A sampled signal x, (t) is obtained using a sampling frequency f,= 50 samples/second. Please find and plot its Fourier transform X, (f). c) Can we reconstruct the signal r(t) from its samples or not? Please also explain why.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

Consider a signal
sin (40πt)
πt
a) Find its Fourier transform defined by using regular frequency
X(f) =
a(t)e-1²*1¹ dt = X(w) |w=2″ f
x(t)
=
b) A sampled signal x, (t) is obtained using a sampling frequency f,= 50 samples/second. Please
find and plot its Fourier transform X, (f).
c) Can we reconstruct the signal r(t) from its samples or not? Please also explain why.

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Step 3: Proof of Fourier transform of sinc(t) function

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Step 4: b) Fourier transform of sampled signal

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