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Random Processes and Spectral Analysis Chap. 6
6–20 Using MATLAB, plot the PSD for a Manchester NRZ line code that has values of ;1 that are
equally likely. Assume that the data are independent from bit to bit and that the bit rate is 9600 b/s.
Hint: Look at your solution for Prob 6–19 or look at Eq. (3–46c).
6–21 The magnitude frequency response of a linear time-invariant network is to be determined from a
laboratory setup as shown in Fig. P6–21. Discuss how |H( f )| is evaluated from the measurements.
White-noise
source
p x (f)=N 0 /2
x(t) Linear network y(t) Spectrum analyzer
H(f) unknown
(measures p y (f))
Figure P6–21
★ 6–22 A linear time-invariant network with an unknown H( f ) is shown in Fig. P6–22.
(a) Find a formula for evaluating h(t) in terms of R xy (t) and N 0 .
(b) Find a formula for evaluating H(f) in terms of xy ( f ) and N 0 .
White-noise
source
p x (f)=N 0 / 2
x (t)
Linear network
H(f) unknown
y (t)
x (t)
Figure P6–22
6–23 The output of a linear system is related to the input by y(t) = h(t) * x(t), where x(t) and y(t) are
jointly wide-sense stationary. Show that
(a) R xy (t) = h(t) * R x (t).
(b) xy (f) = H(f) x (f).
(c) R yx (t) = h(-t) * R x (t).
(d) yx (f) = H * (f) x (f).
[Hint: Use Eqs. (6–86) and (6–87).]
6–24 Using MATLAB, plot the PSD for the noise out of a RC LPF for the case of white noise at the filter
input. Let N 0 = 2 and B 3dB = 3 kHz.
★ 6–25 Ergodic white noise with a PSD of n ( f ) = N 0 2 is applied to the input of an ideal integrator with
a gain of K (a real number) such that H(f) = K(j2pf).
(a) Find the PSD for the output.
(b) Find the RMS value of the output noise.
6–26 A linear system has a power transfer function |H(f)| 2 as shown in Fig. P6–26. The input x(t) is a
Gaussian random process with a PSD given by
|H(f)| 2
1.0
– B B
Figure P6–26
f