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kamalmanzukie
KVRist
 
121 posts since 12 May, 2012

Postby kamalmanzukie; Sat May 12, 2018 5:19 pm subsampling in the frequency domain

does anyone here know what might be some of the conditions surrounding if one was to sample frequency bins at a subharmonic frequency instead of twice per bin or whatever?

i have a guess that it would alias, but that the aliasing would be consonant and thus not so disruptive for analysis?

is that similar to the aliasing you get with wavelet transforms?

thanks so much.
mystran
KVRAF
 
4837 posts since 11 Feb, 2006, from Helsinki, Finland

Postby mystran; Sun May 13, 2018 9:06 am Re: subsampling in the frequency domain

kamalmanzukie wrote:does anyone here know what might be some of the conditions surrounding if one was to sample frequency bins at a subharmonic frequency instead of twice per bin or whatever?


Judging by the fact that there's 52 views and no replies, I suspect I might not be the only one that has trouble understanding what you mean by "sample frequency bins at a subharmonic frequency" exactly? :)

I mean... I'm not even sure if you're thinking about modifying the DFT or just trying to do some spectral processing. As far as spectral aliasing goes, it works the same as regular aliasing, the folding happens in the "other domain" as DFT being (essentially) it's own inverse the choice of "spectrum" vs. "time domain" is mathematically just a matter of definition really.
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stratum
KVRAF
 
1738 posts since 29 May, 2012

Postby stratum; Sun May 13, 2018 11:08 pm Re: subsampling in the frequency domain

If we leave the confusing words aside and try to make sense of that post, this is what I would say:

If you want to increase resolution in frequency domain of a DFT result, then you take a larger window of samples at time domain, and if more samples are not available, then fill the rest of the window with zeros. This doesn't result in aliasing and gives a better resolution at frequency domain. It's like upsampling in time domain, i.e. you can always figure out the intersample values, because the samples are assumed to be taken from a band limited continuous signal.
~stratum~
kamalmanzukie
KVRist
 
121 posts since 12 May, 2012

Postby kamalmanzukie; Mon May 14, 2018 3:26 pm Re: subsampling in the frequency domain

excuse the vagueness. the problem exactly is i'm working with something kind of along the lines of constant q transform, so the bins at the top get sampled more often than the ones at the bottom. the rate that the ones at the top need to be sampled to keep everything kosher gets pretty high up there, to the point that it causes problems for the analysis i'm doing and its not great for cpu either

so what i was wondering is what i might expect if the bins at top were sampled at a rate that was a subharmonic to the required sampling frequency - specifically some number of octaves lower. would the aliasing that was generated be 'masked', so to speak? would it be better to keep them filtered below half the actual bin sample rate?

all i am doing is comparing amplitudes, so i'm not worried about there being subharmonics in any inverse transform, cause im not even doing one.

as far a zero padding goes, i'm not even sure how that would work. i only very recently was able to conceptualize how windowing for constant q looks
mystran
KVRAF
 
4837 posts since 11 Feb, 2006, from Helsinki, Finland

Postby mystran; Mon May 14, 2018 6:13 pm Re: subsampling in the frequency domain

kamalmanzukie wrote:so what i was wondering is what i might expect if the bins at top were sampled at a rate that was a subharmonic to the required sampling frequency - specifically some number of octaves lower. would the aliasing that was generated be 'masked', so to speak? would it be better to keep them filtered below half the actual bin sample rate?


Oh, I see... so what you probably is known as "multi-rate filter banks" which should return you at least a metric ton of Google results. The basic idea is to split the signal into multiple bands of equal bandwidth (eg. most commonly halves) and then decimate each band. Then you can do this recursively until each of your bands is at a resolution suitable for what you want to do.
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kamalmanzukie
KVRist
 
121 posts since 12 May, 2012

Postby kamalmanzukie; Tue May 15, 2018 1:35 pm Re: subsampling in the frequency domain

that's like sub band coding, right? i know there are also ways to start out with a regular old fourier transform and warp it into constant q bandwidth, which i hate

i'm just using old fashioned heterodyning with proper filters and sines/cosines. i just decided to filter below half of whatever rate i'm subsampling and it seems to work fine. it definitely seems that subsampling at some lower octave is generally friendlier than if using some other random frequency, in that it may still add a low frequency image but at least the amplitude measurement is about what it should be

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