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Pulse amplitude modulation (PAM) corresponds to the baseband technique of encoding the information symbols in the amplitude of a pulse in the form: Xpam (t) = a[k]p(t – kTs), k=-∞0 where a[k] = {-1,1} are the equiprobable and uncorrelated information sym- bols, p(t) is the pulse shaping function of duration t € [0,TÂ], and T is the symbol interval. For this waveform: 1. determine the ensemble mean (t) and variance o(t). Is this process first-order cyclostationary? Justify your answer properly. 2. Determine the ensemble autocorrelation function Rä(t₁, t2). Is this pro- cess second-order cyclostationary? Justify your answer properly. 3. Determine an expression for the time-averaged auto-correlation function: 1 RO (7) = — ²² 5.² Rex (t, t - r)dt.

Pulse amplitude modulation (PAM) corresponds to the baseband technique of encoding the information symbols in the amplitude of a pulse in the form: Xpam (t) = a[k]p(t – kTs), k=-∞0 where a[k] = {-1,1} are the equiprobable and uncorrelated information sym- bols, p(t) is the pulse shaping function of duration t € [0,TÂ], and T is the symbol interval. For this waveform: 1. determine the ensemble mean (t) and variance o(t). Is this process first-order cyclostationary? Justify your answer properly. 2. Determine the ensemble autocorrelation function Rä(t₁, t2). Is this pro- cess second-order cyclostationary? Justify your answer properly. 3. Determine an expression for the time-averaged auto-correlation function: 1 RO (7) = — ²² 5.² Rex (t, t - r)dt.

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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Pulse amplitude modulation (PAM) corresponds to the baseband technique of encoding the information symbols in the amplitude of a pulse in the form: Xpam (t)= a[k]p(t – kTÂ), k=-∞ where a[k] € {-1,1} are the equiprobable and uncorrelated information sym- bols, p(t) is the pulse shaping function of duration t € [0,TÂ], and T, is the symbol interval. For this waveform: 1. determine the ensemble mean µ(t) and variance o²(t). Is this process first-order cyclostationary? Justify your answer properly. 2. Determine the ensemble autocorrelation function Rez(t₁, t₂). Is this pro- cess second-order cyclostationary? Justify your answer properly. 3. Determine an expression for the time-averaged auto-correlation function: 1 Ts RO (7) = Rex(t,t-T)dt.
Transcribed Image Text:Pulse amplitude modulation (PAM) corresponds to the baseband technique of encoding the information symbols in the amplitude of a pulse in the form: Xpam (t)= a[k]p(t – kTÂ), k=-∞ where a[k] € {-1,1} are the equiprobable and uncorrelated information sym- bols, p(t) is the pulse shaping function of duration t € [0,TÂ], and T, is the symbol interval. For this waveform: 1. determine the ensemble mean µ(t) and variance o²(t). Is this process first-order cyclostationary? Justify your answer properly. 2. Determine the ensemble autocorrelation function Rez(t₁, t₂). Is this pro- cess second-order cyclostationary? Justify your answer properly. 3. Determine an expression for the time-averaged auto-correlation function: 1 Ts RO (7) = Rex(t,t-T)dt.
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