clear;
f1 = 5; % frequency of the 1st tone, in Hertz
f2 = 2.5; % frequency of 2nd tone, in Hertz
fc = 120; % carrier frequency, in Hertz
t0 = 100; % holding time, in second
ts = 1 / ( 16 * max( [ f1, f2, fc ] ) ); % sampling interval, in second
t = 0 : ts : t0; % sampling time sequence
% f = 0 : 1/ts : 1/t0;
A = sqrt(2); % amplitude of the 1st tone
B = sqrt(2); % amplitude of the 2nd tone
m1 = A*cos(2*pi*f1*t); % 1st tone
m2 = B*sin(2*pi*f2*t); % 2nd tone
subplot( 3, 2, 1) % plot the 1st tone
plot( t, m1 ); grid
xlabel( 'Time [s]' ); ylabel( 'Amplitude' );
title( '1st tone, a cosine wave' );
axis( [ 0 3 -2 2 ] )
subplot( 3, 2, 2 ) % plot the 2nd tone
plot( t, m2 ); grid
xlabel( 'Time [s]' );ylabel( 'Amplitude' );
title( '2nd tone, a sine wave' );
axis([0 3 -2 2])
% m(t)
m = m1 + m2;
subplot( 3, 2, 3 )
plot( t, m ); grid
xlabel( 'Time [s]' ); ylabel( 'Amplitude' );
title( 'Modulating signal' );
axis( [ 0 3 -4 4 ] )
C=2; % amplitude of carrier
c=C*cos(2*pi*fc*t); % plot carrier
subplot(3,2,4)
plot(t,c);grid
xlabel('Time [s]');ylabel('Amplitude');
title('Carrier');
axis([0 0.1 -2 2])
% PSD of the modulating signal
subplot(3,2,5)
fs = 16 * max( [ f1, f2 ] );
ts = 1 / fs; % sampling interval, in second
t = 0 : ts : t0; % sampling time sequence
m1 = A*cos(2*pi*f1*t); % 1st tone
m2 = B*sin(2*pi*f2*t); % 2nd tone
m = m1 + m2;
[cory, lag] = xcorr(m,'unbiased'); % unbiased autocorrelation of modulating signal
lag = lag / fs;
idx = abs( lag ) < 1.5;
plot( lag( idx ), cory( idx ) ); % plot autocorrelation of modulating signal
xlabel( 'lag [s]' ); ylabel( 'ACF' );
title( 'Autocorrelation of modulating signal' );
fc = fft( cory ) / sqrt( length( cory ) )^2;
cm = abs( fftshift( fc ) );
f3= ( - length( fc ) / 2 + 1 : length( fc ) / 2 )' * fs / length( fc );
idx = abs( f3 ) < 6;
subplot( 3, 2, 6 )
stem(f3( idx ),cm( idx ), '.' );grid %自相关函数的傅里叶变换：即功率谱密度。其中。cm是cory付里叶变换后的幅值。f3为fc的长度。
xlabel('Frequency [Hz]'); ylabel('Power');
title('PSD of modulating signal');
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