Mitchell, T. J. (2010) An exploration of evolutionary computation ...

coinciding partials: constructive and destructive interference respectively. If the ratio of the
carrier to modulating frequency is a rational number, these reflections produce an
arithmetic series of sinusoidal partials with frequencies at integer multiples of a
fundamental frequency: the so-called harmonic spectrum. Conversely, when the ratio is
irrational, reflections are positioned between the positive frequency components to produce
a non-harmonic spectrum. With so few parameters with which to control such a wide range
of timbres, combined with the non-linear effects outlined above, FM has become widely
regarded as a difficult synthesis type to control (Kronland-Martinet et al, 2001), (Horner,
2003), (Delprat, 1997), (Payne, 1987). Consequently, a fair proportion of the work in this
thesis is concerned with the development of algorithms that are designed to evolve
solutions to complex real-world multimodal static optimisation problems. Thus, the
fundamental research question that motivates this research is as follows:
Can evolutionary algorithms be created and employed to locate multiple distinct
matches of a given target sound, with conventional frequency modulation audio
synthesis structures?
1.2 Objectives
To introduce the work set out in the following chapters, the principal objectives which
have directed this research are enumerated below.
1. To explore the potential for evolutionary computation as a mechanism for
parameter estimation with frequency modulation synthesis.
2. To assess and develop optimisation algorithms suitable for optimising multiple sets
of frequency modulation synthesis parameters that approximate a given target
sounds.
3. To develop a testing method that enables algorithmic performance to be measured
quantitatively in application to sound matching problems.
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