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OSH Audio THD instrument and live BOM

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rhb:
Actually, Nyquist does not rule, Shannon does.  Compressive sensing evades Nyquist, but not Shannon.  Nyquist addressed the case of regular sampling which results in a convolution in the frequency domain with a spike series.  The Nyquist limit is where the adjacent images of the spectrum overlap.

The attached figure is from "A Mathematical Introduction to Compressive Sensing" by Foucart and Rauhut.  There are 5 sinusoids (top left) that make up the 64 point series (lower left) and those 5 sinusoids are *exactly* recovered (lower right)  with only 16 randomly selected samples.  One more than the Shannon minimum of 15.

The point of sampling all the amplitudes at all the frequencies is to deal with non-linearities.  The variation of the sampling clock will require more thought.  That is a *very* extensively studied problem in reflection seismology as the sources and receivers are never exactly uniformly spaced.  But I think a sparse L1 pursuit would solve it to within 1/f noise.

If you feel any random pains that will be me sticking pins in a voodoo doll of a Norse deity for bringing up the clock variance ;)

ciccio:

--- Quote from: rhb on February 07, 2019, 05:43:05 pm ---Give "Max Wein, Mr. Hewlett and a Rainy Sunday Afternoon"  by Jim Williams a read.

--- End quote ---
Thank you for the citation.
I googled fo it and found some really interesting pages to be read this evening.

rhb:
The attitude towards learning that Jim displays just makes you feel good.  Anything by Jim Williams is a pure delight to read.

Kleinstein:
An analog THD meter can be relatively easy for a single frequency, as the oscillator and notch can be well tuned. It gets way more difficult if the frequency is variable.  Like with the purely digital approach one could correct for some of the source errors - so the limit is at something like 1/10 the source quality, maybe a little better, if the system and DUT is broad band and very stable.

Today I would also prefer the more digital way - it takes quite some effort to make a Wien bridge oscillator as good as a good sound card. 

asgard:
My approach here is to have three representative oscillator/filter pairs switched in, 100Hz, 1KHz, and 10KHz.  All  six modules are tuned to as great an accuracy as I can achieve.  One thing I have been considering lately is how to represent the analysis, either as a result of an FFT executed on the scope, or another simple analog method, which is a peak-detect and hold circuit after the notch filter.  That would only require a multimeter to directly measure the power density of the distorted spectrum.  Again the goal here is not to achieve perfection, which we all know is the enemy of good-enough.  What I wanted to do is to show how an adequately good benchtop instrument can be constructed with a BOM budget of $200 or less.  Also, the point was to show how the project can be managed adequately well using some schmarts in an Excel spreadsheet in a way that scales

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