Nonlinear Wave Synthesis by Lookup Table

In Chapter 2 we looked at concatenative (wavetable) synthesis of music and speech. The idea there was to store pieces of waveforms and join them together in the time domain to make sound. The idea of a loop for periodic sounds (steady state of a trumpet, vowels of speech, etc.) was introduced. One way to 

As an exercise, let s switch the roles of the wavetable and the sawtooth. Storing a linear ramp in the table results in the input simply being passed through to 

Distorting the ramp a little would result in a distortion of the output wave. We can store any shape in the wavetable, resulting in a wide variety of possible outputs. Accessing a wavetable (often a simple waveform) with another (usually simple) waveform is called waveshaping synthesis. 

One common form of waveshaping synthesis, called Frequency Modulation (FM), uses sine waves for both input address and wavetable waveforms. 

Frequency modulation relies on modulating the frequency of a simple periodic waveform with another simple periodic waveform. When the frequency of a sine wave of average frequency(called the carrier) is modulated by another sine wave of frequency (called the modulator), sinusoidal sidebands are created at frequencies equal to the carrier frequency plus and minus integer multiples of the modulator frequency. FM is expressed as  

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