John's Blog

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Synthesizing audio with a stupidly low bit-depth, part 1

January 23, 2022

Prerequsites: sampling, quantization, and fourier bullshit.

It's pretty well known that your audio is going to sound bad if it's sampled at a bit-depth that's too low. The waveforms for most recorded music are very spectrally dense, so unless it's massive, the quantization noise ends up being pretty random.

If you're trying to synthesize a wave, though, quantization noise can lead to some surprising artifacts! This blog post explores what happens when you synthesize a sine wave at a very low bit depth.

For my business card, I needed to synthesize audio using the onboard TCC PWM generator. These days, audio codec chips with 32 bits of depth can be had for under a dollar, so why use the microcontroller's onboard PWM generator? Well...

I wanted my system to have as few ICs as possible; an audio codec chip is another component that can go out of stock and will increase BOM size.
To work with batteries small enough to fit inside the 3.2mm thick form factor, the whole system can't draw more than ~20mW, INCLUDING the speaker. In principle, it's possible to make an audio codec that would only draw a few mW, but I couldn't find one on the market.
Most of the audio codec chips I could find required a minimum operating voltage of 2.7v. The microcontroller I picked (a Microchip/Atmel SAMD10) can operate down to 1.62v. To save power, I'm operating close to this minimum operating voltage (1.8v), and didn't want to include a second voltage level to accomodate another chip.

I needed to synthesize audio with only 4 bits of depth. Because this isn't the early 70's, having an audio synth with only 4 bits of depth seems totally crazy!

TODO: an interactive demo of the freq vs. sampling freq vs. quantization noise would be awesome.

TODO: the graph containing a non-integer number of sine cycles makes the visualization more confusing.

TODO: make it so that they can hear the sounds

Sine frequency
Sample rate

samples per sine period: 110.250

Bit Depth

Wave

Quantization noise

Fourier Transform

key takeaway: unless you're synthesizing a wave with a period that's a multiple of the sampling period, you'll get extra tones in your quantization noise