distortions are images in time before the impulse response

[anyfoo]

I would like to understand how distortion images end up in time before the impulse in the calculated impulse response. I'm interested in the actual math. A quick Google search turns up nothing immediately relevant (though Google has been deteriorating for years, especially when searching for technical subjects). So is there some literature you can directly refer me to?

Thanks!

 

[ddude003]

Maybe you are looking for something like: https://www.aes.org/tmpFiles/elib/20220425/20458.pdf ???

 

[anyfoo]

This looks to be just about sample theory in general, which I'm hopefully already familiar with. I'm specifically looking for literature (or just an explanation) on how non-linearities end up as earlier images when computing the impulse response from a log sweep.

 

[anyfoo]

I think I found the answer here:

CiteSeerX — Transfer-Function Measurement with Sweeps DIRECTOR’S CUT INCLUDING PREVIOUSLY UNRELEASED MATERIAL

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Compared to using pseudo-noise signals, transfer function measurements using sweeps as excitation signal show significantly higher immunity against distortion and time variance. Capturing binaural room impulse responses...

citeseerx.ist.psu.edu

Specifically on page 19:

Consider a sweep that glides through 100 Hz after 100 ms and reaches 200 Hz at 200 ms. To compress this excitation signal to a Dirac pulse, the reference spectrum needs to have a correspondent group delay of -100 ms at 100 Hz and -200 ms at 200 Hz. When the instantaneous frequency is 100 Hz and the DUT produces second order harmonics, a 200 Hz component with the same delay as the 100 Hz fundamental will be present in the DUT’s response. This 200 Hz component will then be treated with the -200 ms group delay of the reference spectrum at 200 Hz and hence appear at -100 ms after the deconvolution process. Likewise, higher-order harmonics will appear at even more negative times.

This is very enlightening and makes intuitive sense. I guess an open question I still have is what happens with distortion products that are lower than the fundamental. Shouldn't those appear as components that have too large a delay and therefore go under in the actual tail of the impulse response, still negatively affecting the interpretation?

 

[ddude003]

Might be interesting to ask Rob Watts over at https://www.head-fi.org/forums/rob-watts.7899/ ... Rob seems to think that a Dirac pulse does not occur in natural music... And his insights into pre-ringing are also interesting...

 

[John Mulcahy]

I guess an open question I still have is what happens with distortion products that are lower than the fundamental. Shouldn't those appear as components that have too large a delay and therefore go under in the actual tail of the impulse response, still negatively affecting the interpretation?

How would such components arise? At any given instant the sweep is at a single frequency, so there is no way to produce intermodulation, only harmonic distortion at multiples of the instantaneous sweep frequency.

 

[anyfoo]

How would such components arise? At any given instant the sweep is at a single frequency, so there is no way to produce intermodulation, only harmonic distortion at multiples of the instantaneous sweep frequency.

Isn't the "distortion" here just anything non-linear done to the signal in general, which can really be anything? I guess we make some (probably reasonable) assumptions about what the distortion is, then?

Maybe it's physically impossible for lower frequencies to appear in "real", analogue systems (I don't know), but then couldn't I in theory at least have, say, a DSP with some buggy non-linear software that decides to output a downmixed signal along the input signal?

EDIT: I guess for distortion we only take functions into account that have a Taylor expansion, which here includes that they are time-invariant, which seems like a very reasonable assumption. If you have such a "crazy" time variant DSP in the mix, you just can't do very meaningful distortion measurements, it modifies the signal beyond what we would call "reproducing" it here.