Digital Sound & Music: Concepts, Applications, & Science, Chapter 6, last updated 6/25/2013
To verify this with an example, you can generate a graph of the sidebands in MATLAB by doing
a Fourier transfer of the waveform generated by AM and plotting the magnitudes of the
frequency components. MATLAB's fft function does a Fourier transform of a vector of audio
data, returning a vector of complex numbers. The abs function turns the complex numbers into a
vector of magnitudes of frequency components. Then these values can be plotted with the plot
function. We show the graph only from frequencies 1 through 600 Hz, since the only frequency
components for this example lie in this range. Figure 6.52 shows the sidebands corresponding the
AM performed in Figure 6.49. The sidebands are at 450 Hz and 460 Hz, as predicted.
fftmag = abs(fft(AM));
Figure 6.52 Frequency components after amplitude modulation in Figure 6.49
Ring Modulation
Ring modulation entails simply multiplying two signals. To create a digital signal using ring
modulation, the Equation 6.2 can be applied.
Equation 6.2 Ring modulation for digital synthesis
Since multiplication is commutative, there's no sense in which one signal is the carrier
and the other the modulator. Ring modulation is illustrated with two simple sine waves in
Figure 6.53. The ring modulated waveform is generated with the MATLAB commands below.
Again, we set amplitudes to 1.
N = 44100;
r = 44100;
n = [1:N];
w1 = 440;
w2 = 10;
rm = sin(2*pi*w1*n/r) .* cos(2*pi*w2*n/r);
axis([1 10000 -2 2]);
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