robert bristow-johnson wrote:> In article c6okrl02rmi@enews3.newsguy.com, Bob Cain at > arcane@arcanemethods.com wrote on 04/28/2004 12:07:(snip regarding DFT)> so you're refuse to say "that it says nothing whatsoever..." or that, if you > would say it, "that it says nothing whatsoever about anything outside that > interval." *that's* a little ambiguous. from the past, i think you believe > that it *does* say something about something outside that interval. no?> if that *is* the case, we have a disagreement whereas i would say that > neither the DFT nor those N samples tell you what is going on outside that > interval. you are welcome to say that it's, say, zero outside that interval > (and then the consequence of that *assumption* is that the DFT is the > sampling of N samples of the DTFT around the unit circle). i insist that > it's an assumption that may be reasonable in some contexts, but neither > those N samples nor the DFT of them give you that information.The use of the DFT instead of the continuous Fourier transform implies the assumption that the function is periodic, and so is its transform. If the function is not periodic, then you should not use a DFT. If you don't like the assumption, don't use the DFT. There are other transforms (and other sets of basis functions) that don't make that assumption. -- glen
CAUTION! was "What is the advantage on high-sampling rate ?"
Started by ●April 23, 2004
Reply by ●April 28, 20042004-04-28
Reply by ●April 28, 20042004-04-28
On 28 Apr 2004 07:21:45 -0700, robert@suesound.co.za (Robert Gush) wrote: (snipped)>> > >Hi Rick, > >I was just curious so I ran the text through a spell-checker and only >found 'analog' as misspelled. Are there others? >Or is it possibly that my spell-checker is set up for South African >English and an American English checker would pick up other errors? > >Regards >RobertHi Robert, this is kind of "nit picky" as we say in the States, but the word "bellow" should have been "below, and the word "continues" should have been "continuous" See Ya', [-Rick-]
Reply by ●April 28, 20042004-04-28
On Wed, 28 Apr 2004 20:03:51 GMT, glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote: (snipped)> >The use of the DFT instead of the continuous Fourier transform >implies the assumption that the function is periodic, >and so is its transform.Hi Glen, Ah, but what you're saying then is that the DFT has no meaning if it's performed on a sequence of samples that are not periodic. That doesn't just doesn't seem, ... well, correct to me. [-Rick-]>If the function is not periodic, then you should not use a DFT. > >If you don't like the assumption, don't use the DFT. > >There are other transforms (and other sets of basis functions) >that don't make that assumption. > >-- glen >
Reply by ●April 29, 20042004-04-29
In article 409051f8.1732282156@news.sf.sbcglobal.net, Rick Lyons at r.lyons@_BOGUS_ieee.org wrote on 04/28/2004 21:06:> On Wed, 28 Apr 2004 20:03:51 GMT, glen herrmannsfeldt > <gah@ugcs.caltech.edu> wrote: > > (snipped) >> >> The use of the DFT instead of the continuous Fourier transform >> implies the assumption that the function is periodic, >> and so is its transform. > > Ah, but what you're saying then is that the DFT > has no meaning if it's performed on a sequence of > samples that are not periodic. That doesn't > just doesn't seem, ... well, correct to me.i'm a little bit with Rick, here. and i'm a big apologist for the *inherent* periodic nature of the DFT.>> If the function is not periodic, then you should not use a DFT.*i* don't even take it that far.>> If you don't like the assumption, don't use the DFT.nor here. i may not like this property of the DFT, but i may need to use it anyway.>> There are other transforms (and other sets of basis functions) >> that don't make that assumption.what would those other transforms BE if it's sampled data from the field that you want to look at its spectrum? you have the same kind of issues with the DCT. my spin is this (and i will rely on anthropomorphizing the mindless operation of the DFT, sorry Rick, it's my crutch): the DFT transforms a periodic, discrete sequence of numbers (that may or may not have been sampled from a continuous-time function of time) with period N to another periodic sequence or numbers of period N. both sequences need only N (possibly complex) numbers to completely describe them, so when you compute a DFT or iDFT, you send it only N numbers. now when you send it N numbers, the DFT "assumes" that they are N contiguous ordered values yanked out of that infinite periodic discrete sequence. even though the DFT (and iDFT) defines all infinite samples of the result, any decent computer implementation of it will only return N values. this is what i mean when i say that the DFT periodically extends the N samples you give it. now if those N samples came from a non-periodic discrete function, the windowing operation and the frequency domain effects of it happen when one selects the N samples before the DFT ever sees it. but what the DFT does to those N samples is periodically extend them forever. doesn't mean you can't use the DFT to look at some non-periodic data. you just have to keep in mind what it (and a separate windowing operation) is doing to it. r b-j
Reply by ●April 29, 20042004-04-29
r.lyons@_BOGUS_ieee.org (Rick Lyons) wrote in message news:<408da2b2.1556340187@news.sf.sbcglobal.net>...> On Mon, 26 Apr 2004 14:03:42 -0700, "Jon Harris" > <goldentully@hotmail.com> wrote: > > >Perhaps a private e-mail question to Dan, or even a post here questioning that articular point would have been a more appropriate first step than a "CAUTION" message that calls his entire paper into doubt. IMHO. > > > >-Jon> I think you are correct. I was too "heavy handed" > when I submitted my post and used the word "Caution"... > I thought Dan was talking about > discrete sequences when he was really talking about > analog signals... > > I realize my original post upset Dan, and I tried to > let him know that I wasn't criticizing his > enginnering skills. I tried to make him feel > a little better, but I don't think I was successful... > [-Rick-]I too think that a private email first would have been better. Or at least some notification to bring to my attention that my paper is being questioned. I found out about it almost accidently. What I saw sounded to me like an ALL my work should be considered less than trustworthy. I would have prefered it if it was said differently. For example: The paper is blah blah blah, but I find some point to be wrong... It turned out that the point was not even wrong. I was upset at first. I was on another NG having some back and forth with some guy that sells 192KHz gear and keeps comming up with all sorts of real crazy arguments in favor of it, than and someone reported that there are othres in various news groups taking issue with what I said. It turned out to be this thread, no more no less. I have no problem talking and listning to technical people. But at least one NG I was on is made of at least 50% non tecnical recording and mastering people, and so a statment like that CAUTION! causes a lot of harm. So of course once it happened I had to spend more time and outside of this NG, all without help. The common ethical way is to let folks know and give them an opertunity to answer. But there was an appology, and I do accept it. BR Dan Lavry
Reply by ●April 29, 20042004-04-29
Rick, I think he just exaggerated a bit, we both know he's aware of the fact that you can also apply the DFT to non-periodic signals. Basically, he's right in saying: don't complain about the screwdriver if you actually need a wrench... :-) Cheers, Stephan r.lyons@_BOGUS_ieee.org (Rick Lyons) wrote in message news:<409051f8.1732282156@news.sf.sbcglobal.net>...> On Wed, 28 Apr 2004 20:03:51 GMT, glen herrmannsfeldt > <gah@ugcs.caltech.edu> wrote: > > (snipped) > > > >The use of the DFT instead of the continuous Fourier transform > >implies the assumption that the function is periodic, > >and so is its transform. > > Hi Glen, > > Ah, but what you're saying then is that the DFT > has no meaning if it's performed on a sequence of > samples that are not periodic. That doesn't > just doesn't seem, ... well, correct to me. > > [-Rick-] > > > >If the function is not periodic, then you should not use a DFT. > > > >If you don't like the assumption, don't use the DFT. > > > >There are other transforms (and other sets of basis functions) > >that don't make that assumption. > > > >-- glen > >
Reply by ●April 29, 20042004-04-29
r.lyons@_BOGUS_ieee.org (Rick Lyons) wrote:> > Hi Robert, > > this is kind of "nit picky" as we say in the > States, but the word "bellow" should have been "below, > and the word "continues" should have been "continuous" > > See Ya', > [-Rick-]And "it's sampled counterpart" should correctly read "its sampled counterpart" and "no more then removal" should read "no more than removal"... All rights reversed. Kind retards, :-) --smb
Reply by ●April 29, 20042004-04-29
Rick Lyons wrote:> On Wed, 28 Apr 2004 20:03:51 GMT, glen herrmannsfeldt > <gah@ugcs.caltech.edu> wrote: > > (snipped) > >>The use of the DFT instead of the continuous Fourier transform >>implies the assumption that the function is periodic, >>and so is its transform. > > > Hi Glen, > > Ah, but what you're saying then is that the DFT > has no meaning if it's performed on a sequence of > samples that are not periodic. That doesn't > just doesn't seem, ... well, correct to me. > > [-Rick-] > > > >>If the function is not periodic, then you should not use a DFT. >> >>If you don't like the assumption, don't use the DFT. >> >>There are other transforms (and other sets of basis functions) >>that don't make that assumption. >> >>-- glenBah! Math! The DFT is a tool. It's not a perfect fit unless the data are periodic, but that doesn't mean it's useless. To improve the fit, we can fudge a bit; windowing is an example. The DFT is what it is and it does what it does. When it's useful, use it; when it's not, don't. If you can't tell, try it and see. If the foo ... no. If the shoe fits, swear by it, and all that. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 29, 20042004-04-29
r.lyons@_BOGUS_ieee.org (Rick Lyons) wrote in message news:<40904f2a.1731564390@news.sf.sbcglobal.net>...> On 28 Apr 2004 07:21:45 -0700, robert@suesound.co.za (Robert Gush) > wrote: > > (snipped)>> my reply snipped> Hi Robert, > > this is kind of "nit picky" as we say in the > States, but the word "bellow" should have been "below, > and the word "continues" should have been "continuous" >Blush - I should have read it ! Thanks Rick. Regards Robert
Reply by ●April 29, 20042004-04-29
Jerry Avins wrote: (I wrote)>>> The use of the DFT instead of the continuous Fourier transform >>> implies the assumption that the function is periodic, >>> and so is its transform.(someone else wrote)>> Ah, but what you're saying then is that the DFT has no meaning if >> it's performed on a sequence of samples that are not periodic. That >> doesn't just doesn't seem, ... well, correct to me.(after I wrote)>>> If the function is not periodic, then you should not use a DFT.>>> If you don't like the assumption, don't use the DFT.>>> There are other transforms (and other sets of basis functions) >>> that don't make that assumption.> Bah! Math! The DFT is a tool. It's not a perfect fit unless the data are > periodic, but that doesn't mean it's useless. To improve the fit, we can > fudge a bit; windowing is an example. The DFT is what it is and it does > what it does. When it's useful, use it; when it's not, don't. If you > can't tell, try it and see. If the foo ... no. If the shoe fits, swear > by it, and all that.Someone in another post wrote: > Basically, he's right in saying: don't complain about the > screwdriver if you actually need a wrench... I think I agree with this, though the more common don't use a wrench when you really need a hammer might be more applicable. There are problems in physics where periodic boundary conditions are used even though the system is not periodic. The math is easier and the results are close enough. If you do solve the problem that way, don't use the answer to find the surface effects. In cases where the problem can be made periodic without significantly changing the results, then there is no reason not to do it. (I have used the example before of my CD player that only has a repeat mode, making a periodic signal out of any CD.) Things are a little different for DST and DCT. DST has the boundary condition that the function is zero on each end, and DCT that the derivative is zero at each end. For DFT a cyclic rotation of the input points is a phase change in the result, but otherwise doesn't affect the result. For DST or DCT the boundary condition can change the result. So, okay, if you understand the effect of periodic boundary conditions you can use DFT for non-periodic signals. -- glen
