WOSU-FM uses a carrier frequency of 90.5 MHz and modulating constant k f = 66,000. The speech signal utter.au is transmitted on this channel. Plot the frequency spectrum of the FM speech signal.

What will be an ideal response?


Analysis:

In MATLABĀ®, run the following script:



clear;

clc;

[sp, fs] = auread('utter.au');

sound(sp,fs);

kf = 66000;

Fc = 90.5e6; % Carrier frequency

Fs = 184e6; % Sampling frequency

t = 0:1/Fs:1-1/Fs;

au = interp1(0:1/fs:1-1/fs,sp,t,'spline');

for i = 1:Fs

s(i) = cos(2*pi*(Fc+ kf*cumsum(au(i)))*t(i));

end

%%

Ss = abs(fftshift(fft(s,98304))/98304);

delta = Fs/length(Ss);

faxis = -Fs/2:delta:Fs/2-delta;

figure(1)

L = length(faxis);

stem(faxis/10^6,Ss)

xlim([90.3 90.7]);

title('Frequency Spectrum of FM Signal');

xlabel('Frequency(MHz)');

ylabel('Spectrum Magnitude');



It plays the audio signal and compute the FM signal. The spectrum of the FM signal is plotted and shown as follows. The peak centers at the carrier frequency, 90.5MHz.

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