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Problems 129
2–82 The signal x1t2 = 0.5 + 1.5 cos ca 2 V is passed through an RC
3 bpt d + 0.5 sin ca 2 3 bpt d
low-pass filter (see Fig. 2–15a) where R = 1 Æ and C = 1 F.
(a) What is the input PSD, x (f)?
(b) What is the output PSD, y (f)?
(c) What is the average normalized output power, P y ?
2–83 The input to the RC low-pass filter shown in Fig. 2–15a is
x(t) = 1.0 + 2.0 cos v x t + 0.5 sin v x t
Assume that the cutoff frequency is f 0 = 1.5f x .
(a) Find the input PSD, x (f).
(b) Find the output PSD, y (f)
(c) Find the normalized average power of the output, y(t).
★ 2–84 Using MATLAB, plot the frequency magnitude response and phase response for the low-pass filter
shown in Fig. P2–84, where R 1 = 7.5 kÆ, R 2 = 15 kÆ, and C = 0.1 mF.
x(t)
R 1
C R 2
Figure P2–84
y(t)
2–85 A comb filter is shown in Fig. P2–85. Let T d = 0.1.
(a) Plot the magnitude of the transfer function for this filter.
(b) If the input is x1t2 =ß1t/T2, where T = 1, plot the spectrum of the output Y(f) .
x(t)
+
–
y(t)
Delay
T d
Figure P2–85
2–86 A signal x1t2 =ß1t - 0.52 passes through a filter that has the transfer function
H1f2 =ß1f/B2. Plot the output waveform when
(a) B = 0.6 Hz.
(b) B = 1 Hz.
(c) B = 50 Hz.
★ 2–87 Examine the distortion effect of an RC low-pass filter. Assume that a unity-amplitude periodic
square wave with a 50% duty cycle is present at the filter input and that the filter has a 3-dB