Q7. A sinusoid wave of frequency vm = 10 kHz is used to frequency modulate a carrier wave of frequency ve = 96 MHz with a a peak frequency deviation Av = 24 kHz. (a) Does this modulation correspond to narrowband or wideband FM? (b) Using the plots of Bessel functions in figure Q7 and the recursive relation for Bessel functions of the first kind, 2n Jn-1(B) + Jn+1(B) Jn(B) or otherwise, determine the relative amplitude of the the carrier and the significant sidebands. (c) Sketch the power spectrum of this FM waveform. (d) State Carson's rule for determining the number of significant sidebands. (e) What is the maximum bandwidth given by Carson's rule for this modulated waveform? (f) Compare the bandwidth of your calculated power spectrum in part (c) with the maxi- mum bandwidth given by Carson's rule. (g) What is the equivalent AM modulation index obtained if this signal is demodulated with a high-pass RC filter discriminator? 1.0 Jo(x) 0.8 - J1(x) 0.6 0.4 0.2 0.0 1 7. 10 () -0.2 -0.4 Figure Q7: Bessel functions of the first kind J,„(x)
Q7. A sinusoid wave of frequency vm = 10 kHz is used to frequency modulate a carrier wave of frequency ve = 96 MHz with a a peak frequency deviation Av = 24 kHz. (a) Does this modulation correspond to narrowband or wideband FM? (b) Using the plots of Bessel functions in figure Q7 and the recursive relation for Bessel functions of the first kind, 2n Jn-1(B) + Jn+1(B) Jn(B) or otherwise, determine the relative amplitude of the the carrier and the significant sidebands. (c) Sketch the power spectrum of this FM waveform. (d) State Carson's rule for determining the number of significant sidebands. (e) What is the maximum bandwidth given by Carson's rule for this modulated waveform? (f) Compare the bandwidth of your calculated power spectrum in part (c) with the maxi- mum bandwidth given by Carson's rule. (g) What is the equivalent AM modulation index obtained if this signal is demodulated with a high-pass RC filter discriminator? 1.0 Jo(x) 0.8 - J1(x) 0.6 0.4 0.2 0.0 1 7. 10 () -0.2 -0.4 Figure Q7: Bessel functions of the first kind J,„(x)
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Transcribed Image Text:Q7. A sinusoid wave of frequency vm = 10 kHz is used to frequency modulate a carrier wave
of frequency ve = 96 MHz with a a peak frequency deviation Av = 24 kHz.
(a) Does this modulation correspond to narrowband or wideband FM?
(b) Using the plots of Bessel functions in figure Q7 and the recursive relation for Bessel
functions of the first kind,
2n
Jn-1(B) + Jn+1(ß)
Jn(B)
or otherwise, determine the relative amplitude of the the carrier and the significant
sidebands.
(c) Sketch the power spectrum of this FM waveform.
(d) State Carson's rule for determining the number of significant sidebands.
(e) What is the maximum bandwidth given by Carson's rule for this modulated waveform?
(f) Compare the bandwidth of your calculated power spectrum in part (c) with the maxi-
mum bandwidth given by Carson's rule.
(g) What is the equivalent AM modulation index obtained if this signal is demodulated
with a high-pass RC filter discriminator?
1.0
Jo(x)
0.8 -
J1(x)
0.6
0.4
0.2
0.0
6.
7.
10
()
-0.2
1
-0.4
Figure Q7: Bessel functions of the first kind J,„(x)
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