Instantaneous frequency detector

[jclsn]

Rework of the pitch detection logic

Pitch detection in xwax

if (zero_crossing == true)
    pitch_filter_update(M_PI/2);
else
    pitch_filter_update(0.0);

Every time a zero crossing is detected (which happens four times per cycle of the sinusoid), the filter is updated and else it is not updated at all, because there is no information.

This has the advantage that you can easily mentally abstract movement if not trained in signal processing, but an actual DSP engineer would never do this. If you only do measurements on zero-crossing and otherwise feed 0.0 into the filter, the output is very noisy. Feeding 0.0 into the filter on most samples makes the velocity degrade to then snap back when a zero-crossing is found.

New approach

1. Turn the signal into clean sinusoids by e.g taking the derivative
2. Compute the phase difference Δφ from the sine-cosine pair
3. Feed the phase difference into the Kalman filter to obtain a smooth dΔφ
4. Compute the instantaneous frequency by

$$f = \frac{d\Delta\Phi}{2\pi}$$

From here on computing the pitch is trivial:

$$pitch = \frac{f}{\mathrm{f}_\mathrm{timecode}}$$

This updates the filter on every sample and achieves faster direction changes. The performance is great and the scratch feeling is way superior!

Some other fixes

• Tunes the Q and R for the Kalman filter to match the new input
• Fixes a division by zero bug in the Kalman filter
• Improves wrapping robustness of the delayline ringbuffer
• Removes the complex mode switching logic, since it added smoothness at the cost of higher sticker drift
• Draws the monitor only when a signal threshold of -40dB is exceeded to not draw noise
• Some minor cleanups and renamings