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Consider the signal x(t) = sinc(4t+2). (a) Assuming that the unit of time (b) Find a numerical value for the energy 1 microsecond, what is the bandwidth of x(t)? x²(t)dt. (c) Find a time domain expression for the output y(t) = (x * h) (t) when x(t) is passed through a filter with impulse response h(t) = sinc(2t — 4). Simplify as much as possible.

Consider the signal x(t) = sinc(4t+2). (a) Assuming that the unit of time (b) Find a numerical value for the energy 1 microsecond, what is the bandwidth of x(t)? x²(t)dt. (c) Find a time domain expression for the output y(t) = (x * h) (t) when x(t) is passed through a filter with impulse response h(t) = sinc(2t — 4). Simplify as much as possible.

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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Consider the signal x(t) = sinc(4t + 2). (a) Assuming that the unit of time is 1 microsecond, what is the bandwidth of x(t)? (b) Find a numerical value for the energy x²(t)dt. -∞ (c) Find a time domain expression for the output y(t) = (x * h)(t) when x(t) is passed through a filter with impulse response h(t) = sinc(2t — 4). Simplify as much as possible. - (d) For u(t) = x(t) sin(30πt+), find and sketch the magnitude of the Fourier transform |Û(ƒ)|. What is the bandwidth of u(t)? (e) Find a time domain expression for the output v(t) = (u ⋆ h)(t) when u(t) is passed through a filter with impulse response h(t) = sinc(2t — 4). Simplify as much as possible.
Transcribed Image Text:Consider the signal x(t) = sinc(4t + 2). (a) Assuming that the unit of time is 1 microsecond, what is the bandwidth of x(t)? (b) Find a numerical value for the energy x²(t)dt. -∞ (c) Find a time domain expression for the output y(t) = (x * h)(t) when x(t) is passed through a filter with impulse response h(t) = sinc(2t — 4). Simplify as much as possible. - (d) For u(t) = x(t) sin(30πt+), find and sketch the magnitude of the Fourier transform |Û(ƒ)|. What is the bandwidth of u(t)? (e) Find a time domain expression for the output v(t) = (u ⋆ h)(t) when u(t) is passed through a filter with impulse response h(t) = sinc(2t — 4). Simplify as much as possible.
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