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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