### Aaron Hexamer (@Aaron45)

Kaz,Your results make sense to me. Your power ratio is always based on time domain samples or DFT frequency samples. So this script is really demonstrating Parseval's...

Purity plot (last 1000).pngPurity plot (first 200).pngpurity.mPurity vs Bin Offset N is 16, f is 0.25 fs.pdfThanks to everyone who took the time to chime in here....

Not a dumb question at all, in fact it's been on my mind too. As you probably know, to compute a DFT coefficient with Goertzel, you iterate one final time with...

Rick, Yes, that is a correct assumption. It's a single frequency point DTFT calculation, most often not at a bin center.

Thank you for this insight, Rick. One reason I use the generalized Goertzel (a DTFT and not DFT) is so I don't have to worry about bin centering. But I think...

Thank you, Kaz. This is kind of what I suspected. Purity > 1 makes no sense. Wondering if this has anything to do with the use of DTFT vs DFT.

Hi Rick,The inputs are all 16 bit samples, and all subsequent computations are done with doubles. Input signals are very often pure sinusoids with some low background...

Its normally very close to 1 (e.g in a low noise scenario, it's typical for the purity to be > 0.999).Goertzel is known to have numerical errors with large input...

I had been studying this which also notes the special treatment of the 0 and nyquist bins: http://www.dspguide.com/ch10/7.htmI can definitely see similar effects...

"Total energy" from time domain is the summation of all the squares of samples Σ(x[n])^2"DTFT energy" is (2/N)*(DTFT magnitude)^2Purity = "DTFT energy" / "Total...

I have an application where I am computing a purity value, because I'm interested in how much noise is present. Since I don't have a full spectrum measurement...

Rick,Here are some error growth numbers comparing the various resonators. They all seem to fit Err = A*N^x, so I'm publishing the x numbers. The ones highlighted...

Hi Rick. Thanks for the suggestion. I have plotted some of these individually (see example below), but I agree that it would be nice to show them in a some comparative...

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