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Problems 567
(c) Plot (S/N) out vs. (S/N) baseband for this system, and compare the plot with the result for FM
broadcasting as shown in Fig. 7–26.
7–46 Compare the performance of two FM systems that use different deemphasis characteristics.
Assume that b f = 5, (m/V p ) 2 = 1 2
, B = 15 kHz, and that an additive white Gaussian noise
channel is used. Find (S/N) out /(S/N) baseband for:
(a) 25-msec deemphasis.
(b) 75-msec deemphasis.
7–47 A baseband signal m(t) that has a Gaussian (amplitude) distribution frequency modulates a transmitter.
Assume that the modulation has a zero-mean value and a peak value of V p = 4s m . The FM
signal is transmitted over an additive white Gaussian noise channel. Let b f = 3 and B = 15 kHz.
Find (S/N) out /(S/N) baseband when
(a) No deemphasis is used.
(b) 75-msec deemphasis is used.
7–48 In FM broadcasting, a preemphasis filter is used at the audio input of the transmitter, and a
deemphasis filter is used at the receiver output to improve the output SNR. For 75-msec emphasis,
the 3-dB bandwidth of the receiver deemphasis LPF is f 1 = 2.1 kHz. The audio bandwidth is
B = 15 kHz. Define the improvement factor I as a function of B/f 1 as
I =
(S>N) out for system with preemphasis–deemphasis
(S>N) out for system without preemphasis–deemphasis
For B = 15 kHz, plot the decibel improvement that is realized as a function of the design parameter
f 1 where 50 Hz 6 f 1 6 15 kHz.
★ 7–49 In FM broadcasting, preemphasis is used, and yet ∆F = 75 kHz is defined as 100% modulation.
Examine the incompatibility of these two standards. For example, assume that the amplitude of a
1-kHz audio test tone is adjusted to produce 100% modulation (i.e., ∆F = 75 kHz).
(a) If the frequency is changed to 15 kHz, find the ∆F that would be obtained ( f 1 = 2.1 kHz).
What is the percent modulation?
(b) Explain why this phenomenon does not cause too much difficulty when typical audio
program material (modulation) is broadcast.
7–50 Stereo FM transmission was studied in Sec. 5–7. At the transmitter, the left-channel audio,
m L (t), and the right-channel audio, m R (t), are each preemphasized by an f 1 = 2.1-kHz
network. These preemphasized audio signals are then converted into the composite baseband
modulating signal m b (t), as shown in Fig. 5–17. At the receiver, the FM detector outputs the
composite baseband signal that has been corrupted by noise. (Assume that the noise comes
from a white Gaussian noise channel.) This corrupted composite baseband signal is demultiplexed
into corrupted left- and right-channel audio signals, m ' L(t) and m ' R(t), each having
been deemphasized by a 2.1-kHz filter. The noise on these outputs arises from the noise at
the output of the FM detector that occurs in the 0- to 15-kHz and 23- to 53-kHz bands. The
subcarrier frequency is 38 kHz. Assuming that the input SNR of the FM receiver is large,
show that the stereo FM system is 22.2 dB more noisy than the corresponding monaural
FM system.
★ 7–51 An FDM signal, m b (t), consists of five 4-kHz-wide channels denoted by C1, C2, ... , C5, as
shown in Fig. P7–51. The FDM signal was obtained by modulating five audio signals (each with
4-kHz bandwidth) onto USSB (upper single-sideband) subcarriers. This FDM signal, m b (t),