I built an audio timegrapher feature for my watch accuracy app, ChronoLog. Professional timegraphers use a piezo contact sensor and can cost upwards of $1,000. I wanted to do it with a phone mic.
The problem: an iPhone's built-in microphone picks up a mechanical watch's tick at about 1.5 dB SNR. The solution turned out to be epoch folding — the same technique radio astronomers use to find pulsars. Stack 100+ tick periods together and you get +20 dB of effective gain, enough to reliably measure rate and beat error.
The post covers the full DSP pipeline — bandpass filtering, epoch folding, autocorrelation (and why it finds harmonics before fundamentals at low SNR), Kalman filtering for convergence — and what I learned from five rounds of device testing.
Awesome writeup! I wonder whether with a real contact mic (Korg offers one for about 20 bucks) you could get much better results. Due to no 3,5mm on phones anymore it might be easier to use a sound-enabled SBC though.
Did you consider trying the iPhone accelerometer? Perhaps lay the phone face down on the table and then lay the watch on the back? Wondering if this would have higher or lower SNR.
I don't think it would work because the accelerometer updates are at too low a frequency. Apple's developer info says:
```
Before you start the delivery of accelerometer updates, specify an update frequency by assigning a value to the accelerometerUpdateInterval property. The maximum frequency at which you can request updates is hardware-dependent but is usually at least 100 Hz.
```
100Hz is way too slow. Presumably some devices go higher but according to the article the peak signal is in the 3kHz to 15kHz range.
If you know the structure of the “tick”, you can apply the technique of a correlation receiver. It can dig up signals below the noise floor and is used in GPS reception.
It uses the built-in one. But as discussed in the article they ran into the problem where even when you try to force using the internal mic, iOS will silently switch to the mic on a pair of AirPods if there's a pair connected.
I've tried these as apps before, and they never worked that well unfortunately. Perhaps the ticks aren't loud enough, or phone mics aren't that great, or background noise gets picked up as ticks, who knows.
I bought and use the item linked below. It's big, and feels like tech straight out of the cold war era, but works great.
This is a fascinating read but what do you do with this information? Is there a threshold at which you need to take the watch apart and fix something or is this just useful info to know about your watch?
It is actually pretty useful if you own a few mechanical watches. Daily rate tells you how annoying the drift will be, beat error can hint that regulation or service is due, and measuring in different positions gives you a decent sanity check on movement health. Even if you never open the watch yourself, it is a much better baseline before taking it to a watchmaker.
It tells you for how long the time displayed by the watch is valid. If a watch loses ten seconds per day, in a month it will be about five minutes off.
The objective is to minimize this number as much as possible. The open source sensor watch has a temperature sensor and software which turns it into a temperature compensated quartz watch. Mine loses time every year instead of every day or every month.
The problem: an iPhone's built-in microphone picks up a mechanical watch's tick at about 1.5 dB SNR. The solution turned out to be epoch folding — the same technique radio astronomers use to find pulsars. Stack 100+ tick periods together and you get +20 dB of effective gain, enough to reliably measure rate and beat error.
The post covers the full DSP pipeline — bandpass filtering, epoch folding, autocorrelation (and why it finds harmonics before fundamentals at low SNR), Kalman filtering for convergence — and what I learned from five rounds of device testing.
``` Before you start the delivery of accelerometer updates, specify an update frequency by assigning a value to the accelerometerUpdateInterval property. The maximum frequency at which you can request updates is hardware-dependent but is usually at least 100 Hz.
```
100Hz is way too slow. Presumably some devices go higher but according to the article the peak signal is in the 3kHz to 15kHz range.
When you say "phone mic" do you mean the embedded one, or an external one?
I bought and use the item linked below. It's big, and feels like tech straight out of the cold war era, but works great.
https://www.amazon.com/gp/aw/d/B0081SSJZG
The objective is to minimize this number as much as possible. The open source sensor watch has a temperature sensor and software which turns it into a temperature compensated quartz watch. Mine loses time every year instead of every day or every month.