Sound Modelling
103
bank of oscillators
FM couple
vowel-like spectra
formant
line 1
2
4
6
8
10
12
14
Number of side frequency
0
5
10
15
Modulation Index
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Figure 9: Bessel functions of the first kind
sin ( - ), these components have to be flipped onto the positive axis and
summed (magnitude and phase) with the components possibly already present
at those frequencies.
Complex carrier
We can have a bank of oscillators sharing a single modulator or, equivalently, a
non-sinusoidal carrier. In this case, each sinusoidal component of the complex
carrier is enriched by side components as if it were the carrier of a simple FM
couple.
One application of FM with a complex carrier is the construction of vowel-
like spectra, as it was demonstrated by Chowning in the eighties. Each partial
of the carrier may be associated with the center of one formant, i.e. a prominent
lobe in the envelope of the magnitude spectrum. For a given person's voice, each
vowel is characterised by a certain frequency distribution of formants.
Exercise
The reader is invited to implement an FM instrument (in, e.g., Octave or pd)
that reproduces the vowel /a/, whose formants are found at 700, 1200, and 2500
Hz. How can a vibrato be implemented in such a way that the formant position
remains fixed?