Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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A transmitter generates message signals that are described by a baseband
stationary random process x(t). The power spectral density (PSD) of x(t) is
shown in Figure Q4-A. The transmission channel is distortionless, but the
receiver is affected by additive noise. The noise signals can be described by a
stationary random process n(t). The PSD of n(t) is flat over the entire
frequency range and is shown in Figure Q4-B.
a. Find the Fourier transform of Sx(t), i.e., the PSD of x(t) with its
variable renamed as t.
b. Use the duality of the Fourier transform and the result in Q4-a, find the
autocorrelation of x(t).
Sx(f)
10-3
0
- f (Hz)
Figure Q4-A
10-9
-104
Sn (f)
0
Figure Q4-B
-f (Hz)
104
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Transcribed Image Text:A transmitter generates message signals that are described by a baseband stationary random process x(t). The power spectral density (PSD) of x(t) is shown in Figure Q4-A. The transmission channel is distortionless, but the receiver is affected by additive noise. The noise signals can be described by a stationary random process n(t). The PSD of n(t) is flat over the entire frequency range and is shown in Figure Q4-B. a. Find the Fourier transform of Sx(t), i.e., the PSD of x(t) with its variable renamed as t. b. Use the duality of the Fourier transform and the result in Q4-a, find the autocorrelation of x(t). Sx(f) 10-3 0 - f (Hz) Figure Q4-A 10-9 -104 Sn (f) 0 Figure Q4-B -f (Hz) 104
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