A signal m(t) = 2 cos ( 2x 10° t) frequency modulates (FM) a 1 MHz carrier to produce a (peak) frequency deviation of 4 kHz. Write the time-domain expression for the resulting FM signal oFMdt)? What is the value of the frequency deviation constant k? What is the bandwidth of the FM signal?

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Q1
A signal m(t) = 2 cos ( 2x 10° t) frequency modulates (FM) a 1 MHz carier to produce a (peak)
frequency deviation of 4 kHz. Write the time-domain expression for the resulting FM signal ordt)?
What is the value of the frequency deviation constant k? What is the bandwidth of the FM signal?
Q2
An angle modulated signal is given by the following expression:
QEM(t) = 5 cos (@t + 40 sin 500nt + 20 sin 1000t + 10sin 2000nt)
a Determine the (peak) frequency deviation 4f, in Hz.
b. Estimate the bandwidth, in Hz, of the angle modulated signal by Carson's rule.
C. If the angle modulated signal is a phase modulated signal with the phase deviation constant, k, is 5
radians per volt, determine the message signal m (t).
d. If the angle modulated signal is a frequency modulated signal with a frequency deviation constant, k
is 20,000 rradians/sec per volt, determine the message signal m(t).
12
Q3
A message signal m(t) = 4 cos 2n 1000t modulates a carrier frequency to produce a frequency
modulated signal with a resulting modulation index (i.e. frequency deviation ratio) of 2.
(a) What is the estimate of the bandwidth of the FM signal ?
(b) The message signal m(t) is replaced by a new message signal
m(t) = 4 cos 2n 1000t + 4 cos 2n 3000t
What is the estimate of the bandwidth of this new FM signal?
(c) The message signal m(t) is replaced by a new message signal
m(t) = 4 cos 27 3000t
What is the estimate of the bandwidth of this new FM signal?
Use Carson's rule in determining the bandwidth of FM signals.
13
Transcribed Image Text:Questions Q1 A signal m(t) = 2 cos ( 2x 10° t) frequency modulates (FM) a 1 MHz carier to produce a (peak) frequency deviation of 4 kHz. Write the time-domain expression for the resulting FM signal ordt)? What is the value of the frequency deviation constant k? What is the bandwidth of the FM signal? Q2 An angle modulated signal is given by the following expression: QEM(t) = 5 cos (@t + 40 sin 500nt + 20 sin 1000t + 10sin 2000nt) a Determine the (peak) frequency deviation 4f, in Hz. b. Estimate the bandwidth, in Hz, of the angle modulated signal by Carson's rule. C. If the angle modulated signal is a phase modulated signal with the phase deviation constant, k, is 5 radians per volt, determine the message signal m (t). d. If the angle modulated signal is a frequency modulated signal with a frequency deviation constant, k is 20,000 rradians/sec per volt, determine the message signal m(t). 12 Q3 A message signal m(t) = 4 cos 2n 1000t modulates a carrier frequency to produce a frequency modulated signal with a resulting modulation index (i.e. frequency deviation ratio) of 2. (a) What is the estimate of the bandwidth of the FM signal ? (b) The message signal m(t) is replaced by a new message signal m(t) = 4 cos 2n 1000t + 4 cos 2n 3000t What is the estimate of the bandwidth of this new FM signal? (c) The message signal m(t) is replaced by a new message signal m(t) = 4 cos 27 3000t What is the estimate of the bandwidth of this new FM signal? Use Carson's rule in determining the bandwidth of FM signals. 13
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