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Re: Audio Filters (sub-minature)
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John Doe
Jun 9, 2016, 10:23:57 AM6/9/16
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Regular troll...
--
bill.sloman ieee.org wrote in news:57ae1aab-2604-4c0c-8b69-4c2e6712b334 googlegroups.com:
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> Date: Thu, 9 Jun 2016 00:07:23 -0700 (PDT)
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> Subject: Re: Audio Filters (sub-minature)
> From: bill.sloman ieee.org
> Injection-Date: Thu, 09 Jun 2016 07:07:23 +0000
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> Xref: mx02.eternal-september.org sci.electronics.design:421036
>
> On Thursday, June 9, 2016 at 2:16:29 PM UTC+10, Tim Williams wrote:
>> "Phil Hobbs" <pcdhSpamMeSenseless electrooptical.net> wrote in message
>> news:-oSdnaHG3cObqcXKnZ2dnUU7-bfNnZ2d supernews.com...
>> > Sure. That's a time-domain implementation, though. For a general M-tap
>> > filter, the work goes like M**2 in the time domain, rather than
>> > k M log(M) in the frequency domain. The best case is when the transform
>> > length is about 2 M, I think.
>>
>> Yeah, the boxcar is a special case because its work goes as O(1) for any
>> length N. :) It has a rather sloppy response (indeed, maximally sloppy, in
>> the sense of TD-FD duality), though.
>>
>> It would be fun to have "stepped pyramid" filters, where the steps are
>> whole, easily-computed numbers (integer multiples or fractions, so they can
>> be calculated easily with just a few shifts and adds/subtracts), but I kind
>> of doubt there are any more useful than the boxcar and 1-3-3-1. (Of course,
>> any cross section of Pascal's triangle will have those properties, but none
>> of them require as few calculation steps relative to the period.)
>>
>> In general, a "stepped pyramid" exhibits miniature sinc lobes, a set for
>> each step. Still, a "better than boxcar to -xx dB" might be worth playing
>> with, hmm.
>>
>> I never played with it much, so there may be interesting things yet to
>> figure out in that space.
>>
>> Anyway, as for O(M^2) vs. O(M lg M), that's just our old Fourier friend at
>> work; numerical multiplication is merely discrete convolution, and since FFT
>> exists*, we can improve the asymptote by this amount.
>>
>> *Proof by laziness: as long as Cooley and Tukey did their work, I don't have
>> to. :^)
>
> Gauss invented it first (in 1805) and Lanczos and Danielson re-invented it in 1942. Cooley and Tukey invented it again in 1965, after computers had become available enough to make the - considerable - computational effort involved practicable.
>
>> (Say, the same tradeoff appears for sorting algorithms! Are those a case of
>> a similar problem class? The commonality would seem to be the ability to
>> recursively divide and conquer.)
>>
>> <snip>
>> > The solution was sort of interesting. The application was looking down
>> > from the ceiling at people shopping, and people are reliably warmer than
>> > floors (at least in places comfortable enough to shop in). Thus I could
>> > apply a positivity constraint to the integrated output: I put in a very
>> > slow negative-going drift, and zeroed out all negative values.
>> >
>> > That made the random checkerboard go away, and gave nice high-SNR
>> > unipolar blobs corresponding to people.
>>
>> Heh, cool. :)
>>
>> They're doing much the same gimmickry today, what with the processor on the
>> FLIR Lepton and related devices, but without the aid of mammals in their
>> imagery, not necessarily.
>>
>> Speaking of things that are warm blooded, I suppose such a thing wouldn't
>> work so well on lizard people. So either the conspiracy theorists are wrong
>> after all ...or you just didn't test the thing in Washington DC, say.
>
> Lizards are warm-blooded, just not as predictably and consistently warm as mammals. Mammals can hibernate, dropping their core body temperature close to ambient, but they wouldn't do it in the middle of a shopping mall, any more than lizard-people would.
>
> --
> Bill Sloman, Sydney
>
>
--
bill.sloman ieee.org wrote in news:57ae1aab-2604-4c0c-8b69-4c2e6712b334 googlegroups.com:
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> Subject: Re: Audio Filters (sub-minature)
> From: bill.sloman ieee.org
> Injection-Date: Thu, 09 Jun 2016 07:07:23 +0000
> Content-Type: text/plain; charset=UTF-8
> Xref: mx02.eternal-september.org sci.electronics.design:421036
>
> On Thursday, June 9, 2016 at 2:16:29 PM UTC+10, Tim Williams wrote:
>> "Phil Hobbs" <pcdhSpamMeSenseless electrooptical.net> wrote in message
>> news:-oSdnaHG3cObqcXKnZ2dnUU7-bfNnZ2d supernews.com...
>> > Sure. That's a time-domain implementation, though. For a general M-tap
>> > filter, the work goes like M**2 in the time domain, rather than
>> > k M log(M) in the frequency domain. The best case is when the transform
>> > length is about 2 M, I think.
>>
>> Yeah, the boxcar is a special case because its work goes as O(1) for any
>> length N. :) It has a rather sloppy response (indeed, maximally sloppy, in
>> the sense of TD-FD duality), though.
>>
>> It would be fun to have "stepped pyramid" filters, where the steps are
>> whole, easily-computed numbers (integer multiples or fractions, so they can
>> be calculated easily with just a few shifts and adds/subtracts), but I kind
>> of doubt there are any more useful than the boxcar and 1-3-3-1. (Of course,
>> any cross section of Pascal's triangle will have those properties, but none
>> of them require as few calculation steps relative to the period.)
>>
>> In general, a "stepped pyramid" exhibits miniature sinc lobes, a set for
>> each step. Still, a "better than boxcar to -xx dB" might be worth playing
>> with, hmm.
>>
>> I never played with it much, so there may be interesting things yet to
>> figure out in that space.
>>
>> Anyway, as for O(M^2) vs. O(M lg M), that's just our old Fourier friend at
>> work; numerical multiplication is merely discrete convolution, and since FFT
>> exists*, we can improve the asymptote by this amount.
>>
>> *Proof by laziness: as long as Cooley and Tukey did their work, I don't have
>> to. :^)
>
> Gauss invented it first (in 1805) and Lanczos and Danielson re-invented it in 1942. Cooley and Tukey invented it again in 1965, after computers had become available enough to make the - considerable - computational effort involved practicable.
>
>> (Say, the same tradeoff appears for sorting algorithms! Are those a case of
>> a similar problem class? The commonality would seem to be the ability to
>> recursively divide and conquer.)
>>
>> <snip>
>> > The solution was sort of interesting. The application was looking down
>> > from the ceiling at people shopping, and people are reliably warmer than
>> > floors (at least in places comfortable enough to shop in). Thus I could
>> > apply a positivity constraint to the integrated output: I put in a very
>> > slow negative-going drift, and zeroed out all negative values.
>> >
>> > That made the random checkerboard go away, and gave nice high-SNR
>> > unipolar blobs corresponding to people.
>>
>> Heh, cool. :)
>>
>> They're doing much the same gimmickry today, what with the processor on the
>> FLIR Lepton and related devices, but without the aid of mammals in their
>> imagery, not necessarily.
>>
>> Speaking of things that are warm blooded, I suppose such a thing wouldn't
>> work so well on lizard people. So either the conspiracy theorists are wrong
>> after all ...or you just didn't test the thing in Washington DC, say.
>
> Lizards are warm-blooded, just not as predictably and consistently warm as mammals. Mammals can hibernate, dropping their core body temperature close to ambient, but they wouldn't do it in the middle of a shopping mall, any more than lizard-people would.
>
> --
> Bill Sloman, Sydney
>
>
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