Digital Sound & Music: Concepts, Applications, & Science, Chapter 6, last updated 6/25/2013
58
N = 44100;
r = 44100;
n = [1:N];
f_m = 10;
f_c = 440;
w_m = 2 * pi * f_m;
w_c = 2 * pi * f_c;
A = 1;
I = 1;
p = A*cos(w_c * n/r + I*sin(w_m * n/r));
plot(p);
axis([1 30000 -2 2]);
wavplay(p, 44100);
The result is graphed in Figure 6.54.
Figure 6.54 Phase modulation using two sinusoidals,
where and
The frequency components shown in Figure 6.55 are plotted in MATLAB with
fp = fft2(p);
figure;
plot(abs(fp));
axis([400 480 0 18000]);
Figure 6.55 Frequency components from phase modulation in Figure 6.54
Phase modulation produces an infinite number of sidebands (many of whose amplitudes are too
small to be detected). This fact is expressed in Equation 6.4.
( ) [ ]
Equation 6.4 Phase modulation equivalence with additive synthesis
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