# Phase Offsets With Web Audio WaveTables

Being a long-time FL Studio user, and a big fan of the Sytrus plugin that comes bundled with it, I thought a fun experiment would be to try to build a simplified version of the harmonic editor that Sytrus offers with the Web Audio API. So I did that (link), and it became a pretty interesting challenge once I hit the point of assigning phase offsets to individual harmonics.

If you’ve read anything about generating simple waveforms with the Web Audio API, then you’ve probably come across 0xFE’s article on generating tones. At first, this seemed like a pretty good option for handling phase offsets, right? Each harmonic is its own node, with a specific processing function for handling the related phase offset. And there’s even some pretty cool libraries available that I could look at for reference, like this one.

Pretty quickly, though, I decided that probably isn’t a very good idea. I had already decided my harmonic editor should support somewhere around 60 harmonics, because that’s roughly what Sytrus does, and that would mean 60 JavaScriptNodes (scriptProcessorNodes) each firing their callback every *n* sample frames? I don’t know how detailed I should be here because I haven’t really established an audience for this blog, but JavaScript is single-threaded, so every time the JavaScriptNodes fire the “audioprocess” event, 60 callbacks would fill the event loop, and my script would fill every index of the output buffer in each callback. There’s no way that’s efficient. So with that, I decided I could probably find a better solution.

Enter WaveTables. Turns out there probably isn’t much better a solution for this problem than wavetables. Constructing a new wavetable lets me define any waveform I want, and I can play that back with a simple OscillatorNode. Building a wavetable isn’t that bad either:

var context = new webkitAudioContext();

var real = new Float32Array(4096);

var imag = new Float32Array(4096);

imag[1] = 1.0;

var wt = context.createWaveTable(real, imag);

// …

myOscillator.setWaveTable(wt);

Building a wavetable relies on supplying the fourier coefficients for the real and imaginary terms. The real coefficients apply to cosine waves, and the imaginary coefficients apply to sine waves. So, above, I’m just setting index 1 of the imaginary coefficients to 1.0, which sets the relative amplitude of the fundamental frequency to 1.0, and because the associated cosine term has a coefficient of 0, the result will just be a simple sine wave. Awesome. Ok what about phase offsets?

var context = new webkitAudioContext();

var real = new Float32Array(4096);

var imag = new Float32Array(4096);

// Lets assume we’re starting with a simple sine wave:

var a1 = 0.0;

var b1 = 1.0;

// Apply a simple rotation to the initial coefficients

var shift = 2 * Math.PI * 0.5; // Shift the waveform 50%

real[1] = a1 * Math.cos(shift) - b1 * Math.sin(shift);

imag[1] = a1 * Math.sin(shift) + b1 * Math.cos(shift);

var wt = context.createWaveTable(real, imag);

// …

myOscillator.setWaveTable(wt);

Yep, that’s it. Applying a simple 2D rotation by the shift amount (in radians) to the initial fourier coefficients yields a phase shifted waveform. I was pretty surprised by how easy it turned out to be. And this means that I can power my synth with just 1 oscillator node, so long as I build the wavetable correctly. Sounds like an efficiency bonus to me!

And that’s all for now. You can check out the end result of this little experiment here, and please leave thoughts or comments if you have them.