How to generate a waveform table for quicker realtime audio synthesis

Question

I developed an app a few months back for iOS devices that generates real-time harmonic rich drones. It works fine on newer devices, but it's running into buffer underruns on slower devices. I need to optimize this thing and need some mental help. Here's a super basic overview of what I'm currently doing:

• Create an "Oscillator Bank" that consists of X number of harmonics (simply calculated from a given fundamental frequency. Nothing fancy here.)
• Inside my DAC function that spits out samples to an iOS audio buffer, I call a "GetNextSample()" function that goes through the bank of sine oscillators, calculates the sample for each one and adds them up. Some simple additive synthesis.
• Enjoy the beauty of the drone.

Again, it works great, until it doesn't. I'd like to optimize this thing so I'm not using brute additive synthesis of real-time calculated sine waves. If I limit the number of harmonics ("banks") to 2, it'll work on the older devices. Not cool. On the newer devices, it underruns around 50 harmonics. Not too bad. But if I want to play multiple drones at once to create some chords, that's too much processing power.... so...

• Should I generate waveform tables to just loop through instead of constant calculation? (I assume yes...)
• Should I convert my usage of double-precision floating point to integer based calculations? (I assume yes...)

And my big algorithmic question (being pretty non-mathematical):

• If I use a waveform table, how do I accurately determine how long the wave/table should be?? In my experience developing this app, if I just go to the end of a period (2*PI) and start over again, resetting the phase back to 0, I get a sound artifact, since I'm force offsetting the phase. In other words, I can't guarantee that one period will give me the right results...

Maybe I'm over complicating things... What's the standard way of doing quick, processor friendly real-time synth of multiple added sines?

I'll keep poking around in the meantime.

Thanks!

Answer 1

Have you (or can you, not an iOS person) increase the buffer size? Might give you enough overhead that you do not need this. Otherwise yes wave-table synthesis is a viable approach. You could calculate a new wavetable from the sum of all the harmonics only when a parameter changes.

Answer 2

I have written such a beast in golang on server side ... for starters yes use single precision floating point

To address table population, I would assure your implementation is solid by having it synthesize a square wave. Visualize the output for each run as you give it each additional frequency (with its corresponding parms of amplitude and phase shift) ... by definition a single cycle is enough as long as you are correctly using enough cycles to cover the time period of a sample

Its important to leverage the knowledge that generating an output curve from an input set of sine waves ( each with freq, amplitude, phase shift) lends itself to doing the reverse ... namely perform a FFT on that output curve to have the api give you its version of the underlying sine waves (again each with a freq, amplitude and phase) ... this will confirm your system is accurate

The name of the process you are implementing is : inverse Fourier transform and there are libraries for this however I too prefer rolling my own