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Time-limited signals cannot be bandlimited, but their rate of decay in the fre- quency domain depends on the sharpness of the transitions in the time domain. For each of the time-limited signals below, estimate the rate of decay of Â(f)| as sf gets large. You should be able to answer this without detailed computation of the Fourier transform. (a) x₁ (t) = (2- |t|) I[-2,2] (t). (b) x₂ (t): |t|I-2,2] (t). = (c) x3 (t) = cos(πt/4) I[-2,2] (t).

Time-limited signals cannot be bandlimited, but their rate of decay in the fre- quency domain depends on the sharpness of the transitions in the time domain. For each of the time-limited signals below, estimate the rate of decay of Â(f)| as sf gets large. You should be able to answer this without detailed computation of the Fourier transform. (a) x₁ (t) = (2- |t|) I[-2,2] (t). (b) x₂ (t): |t|I-2,2] (t). = (c) x3 (t) = cos(πt/4) I[-2,2] (t).

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Time-limited signals cannot be bandlimited, but their rate of decay in the fre- quency domain depends on the sharpness of the transitions in the time domain. For each of the time-limited signals below, estimate the rate of decay of |Â(ƒ)| as |ƒ| gets large. You should be able to answer this without detailed computation of the Fourier transform. (a) x₁(t) = (2 (b) x₂(t) = |t|I-2,2] (t). (c) 23(t) = cos(πt/4)I-2,2] (t). |t|)I-2,2] (t).
Transcribed Image Text:Time-limited signals cannot be bandlimited, but their rate of decay in the fre- quency domain depends on the sharpness of the transitions in the time domain. For each of the time-limited signals below, estimate the rate of decay of |Â(ƒ)| as |ƒ| gets large. You should be able to answer this without detailed computation of the Fourier transform. (a) x₁(t) = (2 (b) x₂(t) = |t|I-2,2] (t). (c) 23(t) = cos(πt/4)I-2,2] (t). |t|)I-2,2] (t).
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