Sunday, June 25, 2017

Digital Noise

This small note argues that temperature resolution matters even if it transports mostly noise. Continued in the post More On Digital Noise.

A number of temperature measurement instruments deliver values rounded to the degree (C or F). Some others deliver one, two or many decimal places. For simple roast logging that does not make much of a difference. For one, those decimals mostly contain noise as the instruments are not precise enough to deliver such a high accuracy, and for the other, values rounded to the degree are good enough to allow for smooth roast graphs.

However, if the rate-of-rise (RoR) signal (the digital variant of the first derivation) is to be calculated from those temperature signals, a low temperature resolution results in high quantification noise (digital noise) that hinder the generation of smooth RoR signals.

To demonstrate the effect of temperature resolution on the RoR computation, I took a roast profile recorded using a Phidgets 1048 meter containing 5 decimals and step-wise rounded the resolution down to 0 decimals. Note that the effect here is only due to the limited temperature resolution. All smoothing or other processing was deactivated in this experiment, single RoR values calculated from consecutive readings, which were taken in 2 second intervals with 5 decimal temporal resolution.

5 Decimals Temperature Resolution

2 Decimals Temperature Resolution

No big difference to the 5 decimals.

1 Decimals Temperature Resolution

0 Decimals Temperature Resolution

In the following the same profiles with Artisans default smoothing enabled. 
  • Smooth Curves: 1 
  • Smooth Deltas: 8 
  • Delta Span: 6 
  • Smooth Spikes: enabled
With smoothing only working with 0 decimals seems to have a clear negative effect. More smoothing would also help here, but smoothing has always the negative effect of loosing information. So better work with high temperature resolution and minimal smoothing instead!

5 Decimals Temperature Resolution (smoothed)

2 Decimals Temperature Resolution (smoothed)

1 Decimals Temperature Resolution (smoothed)

0 Decimals Temperature Resolution (smoothed)

This suggests that one should lookout for temperature meters with at least 1 (Omega 506RA, Voltcraft/Center, most PIDs), but better two decimals temperature resolutions (Probat Probatone), or higher (like the Phidgets 1048/1046, Yocto Thermocouple/RTD). Note on devices that don't offer any decimal, like the Hottop 2k+, activating oversampling which averages two or more readings can somehow compensate for the low temperature resolution. Extending the RoR Delta Span (menu Tools >> Extras, 1st tab) beyond the selected sampling interval, or increasing the sampling interval itself, has a similar effect, effectively extending the temperature resolution by calculating the single RoR values from temperature readings in higher temporal distance.