### Aaron Hexamer (@Aaron45)

BSEE with Masters degree in SW Engineering.

## Re: Purity > 1?

Nice to see that a completely different approach confirms similar results!

## Re: Purity > 1?

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...

## Re: Purity > 1?

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....

## Re: Purity > 1?

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...

## Re: Purity > 1?

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

## Re: Purity > 1?

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...

## Re: Purity > 1?

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.

## Re: Purity > 1?

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...

## Re: Purity > 1?

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...

## Re: Purity > 1?

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...

## Re: Purity > 1?

"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...

## Purity > 1?

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...

## Re: Error Growth for Various Goertzel Resonators

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...

## Re: Error Growth for Various Goertzel Resonators

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...

## Error Growth for Various Goertzel Resonators

I was going to provide an update on this thread:https://www.dsprelated.com/showthread/comp.dsp/236... But I guess I can't make attachments there.  Probably better...

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