tags: synthesizers music synthesis sound ece-402

Wavetable Synthesis

Wavetable synthesis is a method of [digital] [sound synthesis] that pre-computes values of a [waveform] and stores them into a [wave table].

saves computation time and improves [runtime] by storing values of a waveform, rather than computing them for each [sample]

Below is a diagram of a wavetable synthesizer:

Diagram explanation:

$k_{inc}[n]$ is the [index increment], directly dependent on [frequency] (determined by some controller)
- when no sound is played, $k_{inc}[n]$ is 0
for each new output sample, index increment is added to some index variable stored in a single-sample buffer, $z^{-1}$
index is kept into the range of wavetable indices $[0, L)$ using fmod (resulting in index/[phase] wrap)
then, [lookup] is performed using the computed index, using some interpolation strategy of choice
finally, the signal is multiplied by some sample-dependent [amplitude] value $A[n]$, called the amplitude [envelope]
output is represented by $y[n]$

Using discontinuous wavetables (i.e. waveforms with big jumps, like sawtooth waveforms) will result in a rich [spectrum], i.e. full of [harmonics]
- However, this can result in [aliasing], especially at higher frequencies