1. Plot the message signal and its integral on two separate graphs. The sampling interval is t, = 0.0001.
1. Plot the message signal and its integral on two separate graphs. The sampling interval is t, = 0.0001.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please write matlab code with comments.
![Frequency Modulation
The message signal
sinc(100f) |t| < to
m(t) =
otherwise
frequency modulates the carrier c(t) = cos(2nfet), when f. = 250 Hz and to = 0.1.
The frequency-deviation constant is kf = 100. Therefore, the frequency-modulated
signal is
u(t) = cos (2nft + 2nks m(t)dt).
1. Plot the message signal and its integral on two separate graphs. The sampling
interval is t, = 0.0001.
2. Plot the FM signal u(t).
3. Use MATLAB’s Fourier-transform routine to compute and plot the spectra of
m(t) and u(t) on separate graphs.
4. Determine the modulation index, the bandwidth, and the range of the instanta-
neous frequency of u (t).
5. Demodulate the FM signal u(t) to obtain the message signal and compare the
result with the original message signal. The FM signal can be demodulated by
first finding the phase of u (t), i.e., the integral of m(t), which can be differenti-
ated and divided by 2nkf to yield m(t). Use the MATLAB function unwrap.m
to undo the effect of 2T-phase foldings. Comment on how well the demodulated
message signal matches the original message signal m(t).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04094aaf-3523-49cd-b091-e69534797104%2F73bafb10-4a28-4f70-a03c-e038292f8946%2F12lrd6c_processed.png&w=3840&q=75)
Transcribed Image Text:Frequency Modulation
The message signal
sinc(100f) |t| < to
m(t) =
otherwise
frequency modulates the carrier c(t) = cos(2nfet), when f. = 250 Hz and to = 0.1.
The frequency-deviation constant is kf = 100. Therefore, the frequency-modulated
signal is
u(t) = cos (2nft + 2nks m(t)dt).
1. Plot the message signal and its integral on two separate graphs. The sampling
interval is t, = 0.0001.
2. Plot the FM signal u(t).
3. Use MATLAB’s Fourier-transform routine to compute and plot the spectra of
m(t) and u(t) on separate graphs.
4. Determine the modulation index, the bandwidth, and the range of the instanta-
neous frequency of u (t).
5. Demodulate the FM signal u(t) to obtain the message signal and compare the
result with the original message signal. The FM signal can be demodulated by
first finding the phase of u (t), i.e., the integral of m(t), which can be differenti-
ated and divided by 2nkf to yield m(t). Use the MATLAB function unwrap.m
to undo the effect of 2T-phase foldings. Comment on how well the demodulated
message signal matches the original message signal m(t).
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