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The Fourier transform P() of a the basic pulse p(t) used in a certain binary communication is shown in the figure below: P(f) 0.5 f₁=0.8 √₂=1.2 f. MHz-

The Fourier transform P() of a the basic pulse p(t) used in a certain binary communication is shown in the figure below: P(f) 0.5 f₁=0.8 √₂=1.2 f. MHz-

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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The Fourier transform P(f) of a the basic pulse p(t) used in a certain binary communication is shown in the figure below: P(f) 0.5 f₁ = 0.8 f₂ = 1.2 f, MHz → (a) From the shape of P(), explain at what pulse rate this pulse would satisfy Nyquist's first criterion. (b) Assuming that the pulse is a raised-cosine pulse, find its rolloff factor. (c) Find p(t) and verify that this pulse satisfies Nyquist's first criterion in the time domain. (d) Show how rapidly the pulse decays as a function of t, (i.e., what power of t does the envelope obey for large time values).
Transcribed Image Text:The Fourier transform P(f) of a the basic pulse p(t) used in a certain binary communication is shown in the figure below: P(f) 0.5 f₁ = 0.8 f₂ = 1.2 f, MHz → (a) From the shape of P(), explain at what pulse rate this pulse would satisfy Nyquist's first criterion. (b) Assuming that the pulse is a raised-cosine pulse, find its rolloff factor. (c) Find p(t) and verify that this pulse satisfies Nyquist's first criterion in the time domain. (d) Show how rapidly the pulse decays as a function of t, (i.e., what power of t does the envelope obey for large time values).
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