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128
Signals and Spectra Chap. 2
0.05 F
w 1 (t)
1.5 k
180
w 2 (t)
Figure P2–77
2–78 A signal with a PSD of
x (f) =
2
(1/4p) 2 + f 2
is applied to the network shown in Fig. P2–78.
(a) Find the PSD for y(t).
(b) Find the average normalized power for y(t).
2
x(t)
4
0.5 F
y(t)
Figure P2–78
2–79 A signal x(t) has a PSD
x (f) =
K
[1 + (2pf/B) 2 ] 2
where K 7 0 and B 7 0.
(a) Find the 3-dB bandwidth in terms of B.
(b) Find the equivalent noise bandwidth in terms of B.
★ 2–80 The signal x1t2 = e -400pt u1t2 is applied to a brick-wall low-pass filter whose transfer function is
H(f) = e 1, ƒ f ƒ … B
0, ƒ f ƒ … B
Find the value of B such that the filter passes one-half the energy of x(t).
2–81 Show that the average normalized power of a waveform can be found by evaluating the autocorrelation
R w (t) at t = 0. That is, P = R w (0).
[Hint: See Eqs. (2–69) and (2–70).]