The speech signal utter.au is to be amplitude modulated for transmission on an AM commercial radio band in the United States. Plot the frequency spectrum of the AM signal. Use any channel according to its separations and a modulation index ? = 1 in your design.
Find:
Frequency spectrum of the AM signal.
Analysis:
Pick the channel of carrier frequency 530KHz.
In MATLAB®, use the following script to generate the frequency spectrum of AM signal.
clear;
clc;
%%
% speech utterance signal
[sp, fs] = auread('utter.au');
sp=sp(1:fs)';
l=length(sp);
sound(sp,fs);
% Time-domain carrier
Ac = max(sp);
Fc = 530e3;
Fs = 1120e3;
dt = 1/Fs;
t = 0:1/Fs:1-1/Fs;
c = Ac*cos(2*pi*Fc*(0:dt:1-dt));
% % Frequency-domain carrier
% Sc = abs(fft(c,Fs)/Fs);
% Time-domain AM msg
au = interp1(0:1/fs:1-1/fs,sp,t,'spline');
for i = 1:Fs
s(i) = (Ac + au(i))*cos(2*pi*Fc*t(i));
end
% Time-domain AM msg
figure(1)
plot(t,s);
title('Time-domain AM msg');
xlabel('time(sec)');
ylabel('Sampled Data');
% Frequency-domain AM msg
figure(2)
Ss = abs(fftshift(fft(s,Fs))/Fs);
delta = Fs/length(Ss);
faxis = -Fs/2:delta:Fs/2-delta;
plot(faxis/1000,Ss)
xlabel('Frequency(kHz)');
ylabel('Magnitude');
title('Frequency-domain AM msg');
The time-domain amplitude modulated signal is plot as follows. For comparison, the original waveform of utter.au can be found in the solution to Problem 16.9.
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