comp.lang.idl-pvwave archive - RDF feed
type: channel
description: Messages from Usenet group comp.lang.idl-pvwave, compiled by Paulo Penteado
items: Re: bug in IDL's hanning() window-generating function

Re: bug in IDL's hanning() window-generating function
type: item
description: Scott Bennett writes after a long analysis of the Hanning function: > In any case, I think the point Harris made is that a discrete > sampling of a window function should not taper to the same value at > the end that it has at the beginning because to do so would include > the first sample of the *next* period (windowed segment.) So IDL's > hanning() gets it wrong for both even- and odd-length windows. :-( Uh, huh. And how did RSI respond when you contacted them about it? Cheers, David -- David Fanning, Ph.D. Fanning Software Consulting Phone: 970-221-0438 E-Mail: davidf@dfanning.com Coyote's Guide to IDL Programming: http://www.dfanning.com/ Toll-Free IDL Book Orders: 1-888-461-0155
creator: david[2]
date: 2001-08-01T12:20:01-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: David Fanning wrote: > Scott Bennett writes after a long analysis of the Hanning function: > >> In any case, I think the point Harris made is that a discrete >> sampling of a window function should not taper to the same value at >> the end that it has at the beginning because to do so would include >> the first sample of the *next* period (windowed segment.) So IDL's >> hanning() gets it wrong for both even- and odd-length windows. :-( > > Uh, huh. And how did RSI respond when you contacted them > about it? I suspect they would suggest the following workaround: function Harris, n, _EXTRA=extra return, (hanning(n+1, _EXTRA=extra))[0:n-1] end Scott, I've read your post, but I'm not sure I'm getting the point. Tapering from zero to zero seems like good idea to me, the symmetry sort of "feels good". Besides, it is convenient to have the weight of the window at its centre. What exactly is so wrong with it? Jaco PS: I would look it up myself, but I seem to have misplaced IEEE vol. 66 somehow... ---------------- Jaco van Gorkom FOM-Instituut voor Plasmafysica "Rijnhuizen", The Netherlands e-mail: gorkom@rijnh.nl
creator: Jaco van Gorkom
date: 2001-08-01T14:30:29-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: Jaco van Gorkom wrote: > > David Fanning wrote: >> Scott Bennett writes after a long analysis of the Hanning function: >> >>> In any case, I think the point Harris made is that a discrete >>> sampling of a window function should not taper to the same value at >>> the end that it has at the beginning because to do so would include >>> the first sample of the *next* period (windowed segment.) So IDL's >>> hanning() gets it wrong for both even- and odd-length windows. :-( >> >> Uh, huh. And how did RSI respond when you contacted them >> about it? > > I suspect they would suggest the following workaround: > > function Harris, n, _EXTRA=extra > return, (hanning(n+1, _EXTRA=extra))[0:n-1] > end > > Scott, I've read your post, but I'm not sure I'm getting the point. > Tapering from zero to zero seems like good idea to me, the symmetry > sort of "feels good". Besides, it is convenient to have the weight of > the window at its centre. What exactly is so wrong with it? Hello, I think Scott's post underscores the fact that any sort of Fourier analysis is not to be undertaken lightly without fully understanding how any code used works (or is supposed to work) and knowing, in some fashion, what the result should look like in advance. The difference of a point (or a window being a little bit wider etc) can make a *huge* difference in how one interprets or subsequently uses the results in FFT applications. While I'm not dismissing your comments about the good vibrations one typically gets from symmetry (I try to achieve that as much as possible too) I'm going to file Scott's message under the "READ_THESE_FIRST!!!" sub-directory in my FFT code/work directory. :o) paulv -- Paul van Delst A little learning is a dangerous thing; CIMSS @ NOAA/NCEP Drink deep, or taste not the Pierian spring; Ph: (301)763-8000 x7274 There shallow draughts intoxicate the brain, Fax:(301)763-8545 And drinking largely sobers us again. Alexander Pope.
creator: Paul van Delst
date: 2001-08-01T15:10:44-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: Hi Scott A friend and I noticed this several years ago. My recollection is that he reported this to RSI, but they weren't convinced of the problem. Of course, it *is* a (minor) problem. At the time I was playing around with windows (or apodizing functions, or tapers) and wrote some IDL code. It's included below. The "Slepian" window is commented out because it requires something clever with eigenvalues, and the details have escaped me. To see what Scott is talking about, try typing the following two commands: test= FFT_TAPER(512,'hanning',/PLOT) ;correct way test= FFT_TAPER(512,'badhanning',/PLOT) ;IDL way Although this is old code, I would appreciate any comments or bug reports. Have fun. Brian Jackel ;=========================================================== ====== ;distribute freely, ;use at own risk, ;send all bug reports to bjackel@phys.ucalgary.ca ;+ ; NAME: FFT_TAPER ; ; PURPOSE: This function provides a selection of "tapers" (also known ; as "windows" or "apodizing functions") to reduce sidelobe ; leakage when calculating FFT's. ; ; CATEGORY: Time Series Analysis, Signal Processing ; ; CALLING SEQUENCE: Result= FFT_TAPER(Nelements,Windowname,[Parameter]) ; ; INPUTS: ; Nelements the number of elements in the window ie. # of ; elements in the time series to be windowed. ; Must be a positive integer (floats will be rounded). ; ; Windowname a string containing the name of the windowing function ; to use. Not case sensitive, whitespace will be ignored. ; ; OPTIONAL INPUTS: ; Parameter some tapers can be tuned with a parameter value. See ; specific descriptions for details. ; ; KEYWORD PARAMETERS: ; ; PLOT_EXAMPLE if set, the window and amplitude spectrum will ; be plotted ; RETURN_WINDOWLIST if set, Result will be a string array of all ; valid Windownames ; ; ; ; ; ; ; Kaiser-Bessel This taper can be tuned. Set the parameter to ; (Nuttall p89) the desired location (in scaled Lf/pi units) of ; the first null. ie. 2, 3, or 4 ; ; van der Maas This taper can be tun…
creator: Brian Jackel
date: 2001-08-01T17:51:14-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: In article <MPG.15d1a1e0a012bdcd989e44@news.frii.com>, David Fanning <david@dfanning.com> wrote: > Scott Bennett writes after a long analysis of the Hanning function: > >> In any case, I think the point Harris made is that a discrete >> sampling of a window function should not taper to the same value at >> the end that it has at the beginning because to do so would include >> the first sample of the *next* period (windowed segment.) So IDL's >> hanning() gets it wrong for both even- and odd-length windows. :-( > > Uh, huh. And how did RSI respond when you contacted them > about it? > I didn't contact them. I'm disgusted with them after seeing how they cheated my faculty advisor and, when I asked them to rectify their errors, they refused to do so. I recommended to my advisor that he turn the whole matter over to the university's legal counsel. He told me that he was not going to renew the service contract any more, so I doubt he will bother with having the legal counsel deal with it, but either way it will be his decision and it's now out of my hands. Given their denial of service while we had a service contract, I doubt they would do any better now that we no longer have a service contract. Scott Bennett, Comm. ASMELG, CFIAG College of Oceanic and Atmospheric Sciences Oregon State University Corvallis, Oregon 97331 ************************************************************ ********** * Internet: sbennett at oce.orst.edu * *----------------------------------------------------------- ---------* * "Lay then the axe to the root, and teach governments humanity. * * It is their sanguinary punishments which corrupt mankind." * * -- _The_Rights_of_Man_ by Tom Paine (1791.) * ************************************************************ **********
creator: bennetsc
date: 2001-08-02T05:56:27-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: In article <3B681285.B12C4939@fz-juelich.de>, Jaco van Gorkom <j.c.van.gorkom@fz-juelich.de> wrote: > David Fanning wrote: >> Scott Bennett writes after a long analysis of the Hanning function: >> >>> In any case, I think the point Harris made is that a discrete >>> sampling of a window function should not taper to the same value at >>> the end that it has at the beginning because to do so would include >>> the first sample of the *next* period (windowed segment.) So IDL's >>> hanning() gets it wrong for both even- and odd-length windows. :-( >> >> Uh, huh. And how did RSI respond when you contacted them >> about it? > > I suspect they would suggest the following workaround: > > function Harris, n, _EXTRA=extra > return, (hanning(n+1, _EXTRA=extra))[0:n-1] > end > That looks like it should work for Hann, Hamming, and other raised cosine windows. I am not prepared to vouch for that method for all windows. > Scott, I've read your post, but I'm not sure I'm getting the point. > Tapering from zero to zero seems like good idea to me, the symmetry > sort of "feels good". Besides, it is convenient to have the weight of > the window at its centre. What exactly is so wrong with it? > First, remember that a continuous, finite Fourier transform operates over a time (or space, but I'm just going to refer to time) domain of finite length T. The lowest frequency that can be resolved is the one whose period 1/f = T; i.e. one full period takes exactly the length of the time over which the integral operates. So now consider a periodic function at that frequency. Take, for example, a sine function like y = cos(2 pi t/T), where 0 le t lt T. Note that the function begins at cos(0)=1. The assumption underlying the Fourier transform is that the basis functions are all periodic. So the finite Fourier transform is based upon the same assumption, but also that the function value over the time period from 0 to T exactly repeats ad infinitum. Therefore the time period is closed at the startin…
creator: bennetsc
date: 2001-08-02T07:16:28-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: In article <3B681285.B12C4939@fz-juelich.de>, Jaco van Gorkom <j.c.van.gorkom@fz-juelich.de> wrote: > David Fanning wrote: >> Scott Bennett writes after a long analysis of the Hanning function: >> >>> In any case, I think the point Harris made is that a discrete >>> sampling of a window function should not taper to the same value at >>> the end that it has at the beginning because to do so would include >>> the first sample of the *next* period (windowed segment.) So IDL's >>> hanning() gets it wrong for both even- and odd-length windows. :-( >> >> Uh, huh. And how did RSI respond when you contacted them >> about it? > > I suspect they would suggest the following workaround: > > function Harris, n, _EXTRA=extra > return, (hanning(n+1, _EXTRA=extra))[0:n-1] > end > That looks like it should work for Hann, Hamming, and other raised cosine windows. I am not prepared to vouch for that method for all windows. > Scott, I've read your post, but I'm not sure I'm getting the point. > Tapering from zero to zero seems like good idea to me, the symmetry > sort of "feels good". Besides, it is convenient to have the weight of > the window at its centre. What exactly is so wrong with it? > First, remember that a continuous, finite Fourier transform operates over a time (or space, but I'm just going to refer to time) domain of finite length T. The lowest frequency that can be resolved is the one whose period 1/f = T; i.e. one full period takes exactly the length of the time over which the integral operates. So now consider a periodic function at that frequency. Take, for example, a sine function like y = cos(2 pi t/T), where 0 le t lt T. Note that the function begins at cos(0)=1. The assumption underlying the Fourier transform is that the basis functions are all periodic. So the finite Fourier transform is based upon the same assumption, but also that the function value over the time period from 0 to T exactly repeats ad infinitum. Therefore the time period is closed at the startin…
creator: bennetsc
date: 2001-08-02T07:21:40-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: There is no doubt that the IDL supplied hanning window is symmetric but not "fft-symmetric" as it should be for fft processing. I would guess that for most applications this difference will not significantly impact the results, but for situations where there is a large signal to noise ratio ( > 80 dB) with a sinusoidal signal exactly centered in an fft bin there can be major differences between the two windows. Most real world problems (at least that I have come across) dont meet this situation and the observed differences are minor. Of course there is no reason to use the wrong window when the correct one is easily generated. Clay bennetsc@NOSPAMucs.orst.edu wrote: > In article <3B681285.B12C4939@fz-juelich.de>, > Jaco van Gorkom <j.c.van.gorkom@fz-juelich.de> wrote: >> David Fanning wrote: >>> Scott Bennett writes after a long analysis of the Hanning function: >>> >>>> In any case, I think the point Harris made is that a discrete >>>> sampling of a window function should not taper to the same value at >>>> the end that it has at the beginning because to do so would include >>>> the first sample of the *next* period (windowed segment.) So IDL's >>>> hanning() gets it wrong for both even- and odd-length windows. :-( >>> >>> Uh, huh. And how did RSI respond when you contacted them >>> about it? >> >> I suspect they would suggest the following workaround: >> >> function Harris, n, _EXTRA=extra >> return, (hanning(n+1, _EXTRA=extra))[0:n-1] >> end >> > That looks like it should work for Hann, Hamming, and other > raised cosine windows. I am not prepared to vouch for that method > for all windows. > >> Scott, I've read your post, but I'm not sure I'm getting the point. >> Tapering from zero to zero seems like good idea to me, the symmetry >> sort of "feels good". Besides, it is convenient to have the weight of >> the window at its centre. What exactly is so wrong with it? >> > First, remember that a continuous, finite Fourier transform > operates over a time (or space, …
creator: Clay Kirkendall
date: 2001-08-02T13:35:49-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: bennetsc@NOSPAMucs.orst.edu wrote: > > In article <MPG.15d1a1e0a012bdcd989e44@news.frii.com>, > David Fanning <david@dfanning.com> wrote: >> Scott Bennett writes after a long analysis of the Hanning function: >> >>> In any case, I think the point Harris made is that a discrete >>> sampling of a window function should not taper to the same value at >>> the end that it has at the beginning because to do so would include >>> the first sample of the *next* period (windowed segment.) So IDL's >>> hanning() gets it wrong for both even- and odd-length windows. :-( >> >> Uh, huh. And how did RSI respond when you contacted them >> about it? >> > I didn't contact them. I'm disgusted with them after seeing how > they cheated my faculty advisor and, when I asked them to rectify > their errors, they refused to do so. I recommended to my advisor that > he turn the whole matter over to the university's legal counsel. He > told me that he was not going to renew the service contract any more, > so I doubt he will bother with having the legal counsel deal with it, > but either way it will be his decision and it's now out of my hands. > Given their denial of service while we had a service contract, I doubt > they would do any better now that we no longer have a service contract. Oi vey. another future matlab user.... ? :o) -- Paul van Delst A little learning is a dangerous thing; CIMSS @ NOAA/NCEP Drink deep, or taste not the Pierian spring; Ph: (301)763-8000 x7274 There shallow draughts intoxicate the brain, Fax:(301)763-8545 And drinking largely sobers us again. Alexander Pope.
creator: Paul van Delst
date: 2001-08-02T15:42:28-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: FYI: the hanning() routine that I have from matlab (ver 1.4, 1994) is in worse shape than the one provided with IDL. It is symmetric (not fft-symmetric) and it does not even taper to zero. Clay Paul van Delst wrote: > bennetsc@NOSPAMucs.orst.edu wrote: >> >> In article <MPG.15d1a1e0a012bdcd989e44@news.frii.com>, >> David Fanning <david@dfanning.com> wrote: >>> Scott Bennett writes after a long analysis of the Hanning function: >>> >>>> In any case, I think the point Harris made is that a discrete >>>> sampling of a window function should not taper to the same value at >>>> the end that it has at the beginning because to do so would include >>>> the first sample of the *next* period (windowed segment.) So IDL's >>>> hanning() gets it wrong for both even- and odd-length windows. :-( >>> >>> Uh, huh. And how did RSI respond when you contacted them >>> about it? >>> >> I didn't contact them. I'm disgusted with them after seeing how >> they cheated my faculty advisor and, when I asked them to rectify >> their errors, they refused to do so. I recommended to my advisor that >> he turn the whole matter over to the university's legal counsel. He >> told me that he was not going to renew the service contract any more, >> so I doubt he will bother with having the legal counsel deal with it, >> but either way it will be his decision and it's now out of my hands. >> Given their denial of service while we had a service contract, I doubt >> they would do any better now that we no longer have a service contract. > > Oi vey. another future matlab user.... ? :o) > > -- > Paul van Delst A little learning is a dangerous thing; > CIMSS @ NOAA/NCEP Drink deep, or taste not the Pierian spring; > Ph: (301)763-8000 x7274 There shallow draughts intoxicate the brain, > Fax:(301)763-8545 And drinking largely sobers us again. > Alexander Pope.
creator: Clay Kirkendall
date: 2001-08-02T17:53:01-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: bennetsc@NOSPAMucs.orst.edu wrote: > > I didn't contact them. I'm disgusted with them after seeing how > they cheated my faculty advisor and, when I asked them to rectify > their errors, they refused to do so. Wow. Are you sure it was not a misunderstanding? I have never had a problem on a consumer level with RSI. Of course, I am not trying to sparkle an outpour of complains by writing this. Cheers, Pavel
creator: Pavel A. Romashkin
date: 2001-08-02T21:30:04-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: In article <3B6974E4.CBCC8A96@noaa.gov>, Paul van Delst <paul.vandelst@noaa.gov> wrote: > bennetsc@NOSPAMucs.orst.edu wrote: >> >> In article <MPG.15d1a1e0a012bdcd989e44@news.frii.com>, >> David Fanning <david@dfanning.com> wrote: >>> Scott Bennett writes after a long analysis of the Hanning function: >>> >>>> In any case, I think the point Harris made is that a discrete >>>> sampling of a window function should not taper to the same value at >>>> the end that it has at the beginning because to do so would include >>>> the first sample of the *next* period (windowed segment.) So IDL's >>>> hanning() gets it wrong for both even- and odd-length windows. :-( >>> >>> Uh, huh. And how did RSI respond when you contacted them >>> about it? >>> >> I didn't contact them. I'm disgusted with them after seeing how >> they cheated my faculty advisor and, when I asked them to rectify >> their errors, they refused to do so. I recommended to my advisor that >> he turn the whole matter over to the university's legal counsel. He >> told me that he was not going to renew the service contract any more, >> so I doubt he will bother with having the legal counsel deal with it, >> but either way it will be his decision and it's now out of my hands. >> Given their denial of service while we had a service contract, I doubt >> they would do any better now that we no longer have a service > contract. > > Oi vey. another future matlab user.... ? :o) > Who knows? It will depend upon which package, if any, my next employer wants me to use. I don't even know what my chances are of ever being involved in time series data analysis work again after I finish this degree program. (I suppose, if I can find a suitable disk drive to replace the one that died on my ancient NeXT, I could mess around with Mathematica 3.02 at home... :-) Scott Bennett, Comm. ASMELG, CFIAG College of Oceanic and Atmospheric Sciences Oregon State University Corvallis, Oregon 97331 ***********************************************…
creator: bennetsc
date: 2001-08-03T01:00:41-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: In article <3B69C65C.74C8539D@noaa.gov>, Pavel A. Romashkin <pavel.romashkin@noaa.gov> wrote: > bennetsc@NOSPAMucs.orst.edu wrote: >> >> I didn't contact them. I'm disgusted with them after seeing how >> they cheated my faculty advisor and, when I asked them to rectify >> their errors, they refused to do so. > > Wow. Are you sure it was not a misunderstanding? I have never had a > problem on a consumer level with RSI. Of course, I am not trying to > sparkle an outpour of complains by writing this. My advisor got a couple of IDL licenses back at IDL 5.0, one for his Mac and one for a Sun, which is the one I use. After 5.1 came out, the only way we found out about it was when we heard and read that other sites had gotten their updates and were using them. Later, we got 5.2, which came as a CDROM and a small book titled _What's_ New_in_IDL_5.2?_. However, that book only covered changes between 5.1 and 5.2, so I didn't have what I needed to start using 5.2 if it were installed. Eventually, we heard that other people had gotten their 5.3 updates, but we never got one of those either. Other people in our college also have IDL licenses, so I was able to get the college's computer/networking support folks to install 5.3 and we did get a license string from RSI for it. However, without up-to-date documentation, especially on changes all the way from 5.0 to 5.3, it was not practical to proceed from 5.0. I don't recall whether I had contacted RSI before this time about missing releases and lack of documentation, but at this point I certainly did. My first attempt was ignored. After waiting more than adequate time for response from corporate staff that might be backlogged, I tried again and got a response from a "Technical Support Engineer," who claimed to have forwarded my message to our "maintenance rep" and also claimed there would be a charge if we wanted the manuals we were already supposed to have gotten. (She didn't mention the CDROMs.) No word was ever received from the…
creator: bennetsc
date: 2001-08-03T01:42:23-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: Without making any comment on your problems with RSI, I can say that at least the 5.3 and 5.4 releases (and possibly earlier?) have included all the IDL documentation in PDF format, which in my experience is vastly superior to either the paper manuals or the old help system. Also, you can always download the latest version of IDL (including the documentation) from the RSI web site. We have always found it easy to install updates. Ken Bowman
creator: Kenneth P. Bowman
date: 2001-08-03T02:32:30-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: Scott Bennett writes: > They simply cheated my advisor and > refused to make good when confronted with the facts. I don't know. Pretty strong words for what appears from the facts you present to be a misunderstanding to me. But I know from personal experience that educational institutions are extremely difficult to work with. The left hand never seems to know what the right hand is doing. The people in charge of purchasing the software never seem to have a clue who is using it. Hence, information like where the manuals are and what the terms of the deal are are forever being lost. And the people at educational institutions can be difficult. I'm still livid over a deal I did at a large university in Arizona. They wanted cheap software. I went to bat for them, stuck my neck WAY out to make it happen, and then found myself accused in this newsgroup of being a "software junkie", since I had clearly lowered the price to get them "hooked" on the software. Scheesh! After that experience I spent a couple of years saying to hell with educational institutions. It goes both ways. Cheers, David P.S. Let's just say having the manuals probably wouldn't have helped as much as you think. You would be better off with a good book. There are several now. -- David Fanning, Ph.D. Fanning Software Consulting Phone: 970-221-0438 E-Mail: davidf@dfanning.com Coyote's Guide to IDL Programming: http://www.dfanning.com/ Toll-Free IDL Book Orders: 1-888-461-0155
creator: david[2]
date: 2001-08-03T03:31:56-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: In article <020820012132307408%kbowman@null.net>, Kenneth P. Bowman <kbowman@null.net> wrote: > > Without making any comment on your problems with RSI, I can say that at > least the 5.3 and 5.4 releases (and possibly earlier?) have included > all the IDL documentation in PDF format, which in my experience is > vastly superior to either the paper manuals or the old help system. I looked at the 5.3 stuff in PDF format, but my recollection is that it was broken up into lots of very small files, very inconvenient and expensive to print hardcopy manuals, which then would have had to be punched and put into binders in order to be usable. Since we were supposed to have received the update information anyway, it's not a grad student's place to squander resources on it. The IDL 5.0 help system is nearly worthless. Perhaps the later versions' help systems are better, but they would still be a grossly inefficient and frustrating way of finding out what had changed from version to version. > > Also, you can always download the latest version of IDL (including the > documentation) from the RSI web site. We have always found it easy to > install updates. > I'm a grad student here. Installation of large software packages with licensing schemes is reserved to the college's computer support staff. FWIW, I would like someday, preferably in the very near future, to finish this degree. It's a bit late in the process for me to devote much effort to switching releases at this point. Scott Bennett, Comm. ASMELG, CFIAG College of Oceanic and Atmospheric Sciences Oregon State University Corvallis, Oregon 97331 ************************************************************ ********** * Internet: sbennett at oce.orst.edu * *----------------------------------------------------------- ---------* * "Lay then the axe to the root, and teach governments humanity. * * It is their sanguinary punishments which corrupt mankind." * * -- _The_Rights_of_Man_ by Tom Paine (1791.) * **************************…
creator: bennetsc
date: 2001-08-04T05:26:27-00:00

Re: bug in IDL's hanning() window-generating function
type: item
description: bennetsc@NOSPAMucs.orst.edu wrote: > Jaco van Gorkom <j.c.van.gorkom@fz-juelich.de> wrote: >> function Harris, n, _EXTRA=extra >> return, (hanning(n+1, _EXTRA=extra))[0:n-1] >> end >> > That looks like it should work for Hann, Hamming, and other > raised cosine windows. I am not prepared to vouch for that method > for all windows. Well, I inherited *some* of the functionality from the built-in HANNING() function. Therefore this is not very likely to produce other types of windows, symmetric or not. > So a Hann window, and other windows I've seen so far, should not > include a repetition of its first coefficient as the last coefficient. Thanks to all for the explanations and examples. I am now definitely a convert to 5.5-style hanning windows. Even though I will certainly never encounter an 80 dB signal-to-noise ratio... Jaco
creator: Jaco van Gorkom
date: 2001-08-10T16:16:13-00:00