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A filter has impulse response h(t) = 4sinc(2t)sinc(4t) sin 44πt. (a) Find the transfer function Â(ƒ) and sketch its magnitude. (b) Consider the signal x(t) = 2sinc(4t) cos 40πt. Find and sketch the magnitude |Â(f)| of its Fourier transform. (c) Let y(t) = (x* h) (t) denote the output signal when the signal r(t) is passed through the filter h(t). Find and sketch the magnitude |Ỹ(f)] of its Fourier transform. r∞ 2.(+) d

A filter has impulse response h(t) = 4sinc(2t)sinc(4t) sin 44πt. (a) Find the transfer function Â(ƒ) and sketch its magnitude. (b) Consider the signal x(t) = 2sinc(4t) cos 40πt. Find and sketch the magnitude |Â(f)| of its Fourier transform. (c) Let y(t) = (x* h) (t) denote the output signal when the signal r(t) is passed through the filter h(t). Find and sketch the magnitude |Ỹ(f)] of its Fourier transform. r∞ 2.(+) d

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
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A filter has impulse response \( h(t) = 4 \text{sinc}(2t) \text{sinc}(4t) \sin 44 \pi t \). (a) Find the transfer function \( \hat{H}(f) \) and sketch its magnitude. (b) Consider the signal \( x(t) = 2 \text{sinc}(4t) \cos 40 \pi t \). Find and sketch the magnitude \( |\hat{X}(f)| \) of its Fourier transform. (c) Let \( y(t) = (x \ast h)(t) \) denote the output signal when the signal \( x(t) \) is passed through the filter \( h(t) \). Find and sketch the magnitude \( |\hat{Y}(f)| \) of its Fourier transform. (d) Compute \( \int_{-\infty}^{\infty} x^2(t)dt \), the energy of the input signal. (e) Compute \( \int_{-\infty}^{\infty} y^2(t)dt \), the energy of the output signal.
Transcribed Image Text:A filter has impulse response \( h(t) = 4 \text{sinc}(2t) \text{sinc}(4t) \sin 44 \pi t \). (a) Find the transfer function \( \hat{H}(f) \) and sketch its magnitude. (b) Consider the signal \( x(t) = 2 \text{sinc}(4t) \cos 40 \pi t \). Find and sketch the magnitude \( |\hat{X}(f)| \) of its Fourier transform. (c) Let \( y(t) = (x \ast h)(t) \) denote the output signal when the signal \( x(t) \) is passed through the filter \( h(t) \). Find and sketch the magnitude \( |\hat{Y}(f)| \) of its Fourier transform. (d) Compute \( \int_{-\infty}^{\infty} x^2(t)dt \), the energy of the input signal. (e) Compute \( \int_{-\infty}^{\infty} y^2(t)dt \), the energy of the output signal.
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