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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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).
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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