Algo for rms computation?

After a little digging, I'm to do autocorrelation and finding the peaks. Would autocorrelation be as good use of the CPU resources as FFT?

It turns out autocorrelation can be easily calculated by FFT/IFFT, per  Wiener-Khinchin. I’m onto something!

What's wrong with:

sample (at 500kHz)       s

square (at 500kHz)       sq = s * s

mean (at 500kHz)         m = m + ( (sq - m) /  Ki)

square root (at read out rate)  rms = m ^ 0.5

Division by a constant can be done by multiplication by a constant and a shift operation.

So you need 3 multiplies, 1 add, 1 subtract and 1 shift at sample speed, and the square root at read out speed.

MK

It sounds like you're trying to measure frequency, although I wasn't sure why. All the decent methods I can think of for measuring frequency would take time to compute : ( For instance by first getting the highest amplitude frequency bucket, and then sweeping inside that bucket using an algorithm.

Unrelated, I was thinking that it could be possible to make a simple true RMS meter (nowhere near your desired spec) by using a cheap DSP module. There's a basic example here (Example 7):

 Wave Miner: 10 Experiments with a Pi Digital Signal Processor (DSP) 

It could be completely standalone with that chip incidentally, if the web interface were replaced with a panel meter or moving-coil meter (i.e. all the code residing in the DSP chip). Admittedly very crude, but maybe interesting for those who don't have such a feature in their multimeter.

Also, the measurement bandwidth could be selected by buttons instead of the web interface too (not sure of the use-case, I only did that feature because it was easy in the DSP).

Interesting chip!

I didn't see the cycle counts for the math co-processor but it looks interesting.

Yes, it is interesting. TI is selling the EVB for $16 direct. The part is very much a new item, TI is not sampling it yet. The accelerator is cool, but not as advanced as the MSP430's LEA. 
The benefit for me is no need for noisy SPI bus between ADC and CPU, and I can treat the MCU, once programmed, as a single part RMS converter.

I think the algorithm with Ki used to be referred as exponential decay averaging. The alternative, the moving averaging has a sensitivity when the weight of the partial periods start to influence the average. It happens on the lowest end of the spectrum.

My gut feeling is the exponential decay has the same problem, probably tunable by Ki for the expense of return to zero time, when the signal is removed.

To address the low frequency accuracy concerns, I would experiment with reducing the sampling rate, if the signal is periodic and not much spectral power over let's say fsample/200. This is where autocorrelation and/or FFT comes in. Luckily, it's not much trouble to simulate in a Jupyter notebook.

I'll be very interested to see how you get on with this. My own (limited) experiments in this direction have suggested that the ex. dec. has the advantage of stability and predictability but that more tuned methods which make assumptions or self modifications based on the signal may give very good results with some signals but can be caught out by others. My work was done on ST32H7 series processors which have the advantage of 16bit ADCs (not the best 16 bits I've ever seen) and the 400MHz 64 bit FP possibly makes up for the lack of the accelerator.

I'm still working on the indirectly heated thermistor concept (which is an almost perfect physical analogue of the process I described above) but in reality it trades one kind of complexity (ADC, memory and maths) for a probably more expensive complexity in terms of insulation , heaters and thermal control . But I have other reasons for being interested in the thermal control aspects so it remains a useful project to me.

MK

If the TI part piqued your interest then there is STM32G431. It has single precision float, CORDIC and FMATH accelerators, imo better than IT's offering. 

What I liked about the TI part is that it's so cheap !

I have  a project for a client in mind where it's a prefect fit (and the cheapness matters).

I've ordered a couple of the eval boards.

MK