A 1kHz sinusoidal signal frequency modulates (FM) a carrier at fc=185.3MHz with a peak frequency deviation of 5kHz. The
Posted: Thu May 05, 2022 2:09 pm
A 1kHz sinusoidal signal frequency modulates (FM) a carrier at
fc=185.3MHz with a peak frequency deviation of 5kHz. The
signal peak amplitude is Ac=1V.
m(t)=cos2π×103t V
I) What is the modulation index?
II) Using Carson’s rule, evaluate the approximate bandwidth of the
FM signal.
III) Evaluate the exact magnitude spectra of the FM signal. Sketch
your results. See the attached table for reference. Please only
plot f > fc. (not need to draw the amplitude of each Dirac delta
function very precisely) but label the magnitude of each
Dirac delta function. Draw at least 1kHz higher than the bandwidth
approximated by Carson’s rule.
IV) Compare your spectral plot with the approximate bandwidth of
the FM signal based on Carson’s rule. Calculate the percentage of
power contained in the bandwidth from Carson’s rule
approximation.
n B = 0.1 0 0.998 1 0.050 2 0.001 3 4 5 6 7 8 9 10 2123456 11 B = 0.2 0.990 0.100 0.005 B = 0.5 0.938 0.242 0.031 B = 1 0.765 0.440 0.115 0.020 0.002 B = 2 0.224 0.577 0.353 0.129 0.034 0.007 0.001 B = 5 B = 8 B = 10 -0.178 0.172 -0.246 -0.328 0.235 0.043 0.047 -0.113 0.255 0.365 -0.291 0.058 0.391 -0.105 -0.220 0.261 0.186 -0.234 0.131 0.338 -0.014 0.053 0.321 0.217 0.018 0.223 0.318 0.006 0.126 0.292 0.001 0.061 0.207 0.026 0.123 0.010 0.063 0.003 0.029 0.001 0.012 0.004 0.001 n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 456
fc=185.3MHz with a peak frequency deviation of 5kHz. The
signal peak amplitude is Ac=1V.
m(t)=cos2π×103t V
I) What is the modulation index?
II) Using Carson’s rule, evaluate the approximate bandwidth of the
FM signal.
III) Evaluate the exact magnitude spectra of the FM signal. Sketch
your results. See the attached table for reference. Please only
plot f > fc. (not need to draw the amplitude of each Dirac delta
function very precisely) but label the magnitude of each
Dirac delta function. Draw at least 1kHz higher than the bandwidth
approximated by Carson’s rule.
- A 1khz Sinusoidal Signal Frequency Modulates Fm A Carrier At Fc 185 3mhz With A Peak Frequency Deviation Of 5khz The 1 (132.73 KiB) Viewed 34 times
the FM signal based on Carson’s rule. Calculate the percentage of
power contained in the bandwidth from Carson’s rule
approximation.
n B = 0.1 0 0.998 1 0.050 2 0.001 3 4 5 6 7 8 9 10 2123456 11 B = 0.2 0.990 0.100 0.005 B = 0.5 0.938 0.242 0.031 B = 1 0.765 0.440 0.115 0.020 0.002 B = 2 0.224 0.577 0.353 0.129 0.034 0.007 0.001 B = 5 B = 8 B = 10 -0.178 0.172 -0.246 -0.328 0.235 0.043 0.047 -0.113 0.255 0.365 -0.291 0.058 0.391 -0.105 -0.220 0.261 0.186 -0.234 0.131 0.338 -0.014 0.053 0.321 0.217 0.018 0.223 0.318 0.006 0.126 0.292 0.001 0.061 0.207 0.026 0.123 0.010 0.063 0.003 0.029 0.001 0.012 0.004 0.001 n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 456