Much unlike waveforms, which can only convey limited information on how a signal sounds, spectra, to some extent, reflect the way we perceive sound, and therefore the shape of a spectrum is a very straightforward indication of how a signal will sound. This explains why spectral synthesis techniques are very common. Here we will assume that the reader is already accustomed with basic techniques, such as additive or subtractive synthesis and amplitude/frequency modulation, and rather emphasize less obvious ways to synthesize or manipulate spectra.
The most straightforward way to synthesize a custom spectrum would be to simply aggregate individual signals of a known spectral content together. The idea is obviously following the well-known additive synthesis paradigm, yet we extend this stratagem here to any kind of signal and not merely sinusoids. In such a context, we can use pure sine waves to pointillistically add specific...