Hi People. I recall a discussion here a few months ago where one of us (Robert, perhaps?) posted a reference to very high dynamic range windows -- 100 or 120 dB or so, much higher than a Nutall window. Turns out I now need one of these. (Don't ask. I've been avoiding it but it will not go away.) Can anyone recall this information and re-post it? Thanks much Steve
help -- Windzilla (high dynamic range windows)
Started by ●October 21, 2010
Reply by ●October 21, 20102010-10-21
On Oct 21, 6:58�am, spop...@speedymail.org (Steve Pope) wrote:> Hi People. > > I recall a discussion here a few months ago where one of us > (Robert, perhaps?) posted a reference to very high dynamic range windows -- > 100 or 120 dB or so, much higher than a Nutall window. > > Turns out I now need one of these. �(Don't ask. �I've been avoiding > it but it will not go away.) �Can anyone recall this information and > re-post it? > > Thanks much > > SteveHello Steve, Dale Dalrymple, who posts here often, did this presentation at the last comp.dsp conference. This may have what you need. http://www.compdsp.com/presentations/Dalrymple/dbd.pdf IHTH, Clay
Reply by ●October 21, 20102010-10-21
On 10/21/2010 3:58 AM, Steve Pope wrote:> Hi People. > > I recall a discussion here a few months ago where one of us > (Robert, perhaps?) posted a reference to very high dynamic range windows -- > 100 or 120 dB or so, much higher than a Nutall window. > > Turns out I now need one of these. (Don't ask. I've been avoiding > it but it will not go away.) Can anyone recall this information and > re-post it? > > Thanks much > > SteveSteve, Dale's survey is surely worth looking at. He has some of the better graphs that I've seen. What do *you* mean by "dynamic range" in this context? What are the technical spec's: - performance / main lobe, sidelobes? - implementation? etc. Fred
Reply by ●October 21, 20102010-10-21
Clay <clay@claysturner.com> wrote:>Dale Dalrymple, who posts here often, did this presentation at the >last comp.dsp conference. This may have what you need. > >http://www.compdsp.com/presentations/Dalrymple/dbd.pdfThanks, Clay and Dale. Steve
Reply by ●October 23, 20102010-10-23
Fred Marshall <fmarshall_xremove_the_xs@xacm.org> wrote:>Dale's survey is surely worth looking at. He has some of the better >graphs that I've seen. > >What do *you* mean by "dynamic range" in this context? > >What are the technical spec's: >- performance / main lobe, sidelobes? >- implementation?My purpose is to analyze a signal via simulation so as to determine the compliance of its PSD to a regulatory mask. I am using the term "dynamic range" informally to refer to how far down in the stopband the artifact of the window is. A Dolph-Chebyshev window with -100 dB sidelobes did not, on first attempt, give a lower artifact than the Nuttall-Blackman window I have been using. I have the results I need for the requirement at hand, but I'm generally interested in learning if there's a good way of doing what I'm trying to do, that can resolve to -80 dBc or so in the stopband. Steve
Reply by ●October 23, 20102010-10-23
On Oct 23, 4:17=A0pm, spop...@speedymail.org (Steve Pope) wrote:> Fred Marshall =A0<fmarshall_xremove_the...@xacm.org> wrote: > > >Dale's survey is surely worth looking at. =A0He has some of the better > >graphs that I've seen. >especially the ones on pages 9 and 12 and 19. their really sexy. (colorful and squiggly. i haven't the foggiest about significance yet, i haven't read the paper, but i will look at it now.)> >What do *you* mean by "dynamic range" in this context? > > >What are the technical spec's: > >- performance / main lobe, sidelobes? > >- implementation? > > My purpose is to analyze a signal via simulation so as to determine > the compliance of its PSD to a regulatory mask. =A0I am using the term > "dynamic range" informally to refer to how far down in the stopband > the artifact of the window is.doesn't that have something to do with the length of window? and what you define as acceptable in the passband and transition band? i really need to look at this paper. BTW, Steve, the only window stuff i know anything about is about complementary windows we use in overlap-add synthesis. the Hann window is the most typical example. windows such as the Kaiser ain't complementary. other than that, i know diddley. r b-j
Reply by ●October 24, 20102010-10-24
On 10/23/2010 1:17 PM, Steve Pope wrote:> Fred Marshall<fmarshall_xremove_the_xs@xacm.org> wrote: > >> Dale's survey is surely worth looking at. He has some of the better >> graphs that I've seen. >> >> What do *you* mean by "dynamic range" in this context? >> >> What are the technical spec's: >> - performance / main lobe, sidelobes? >> - implementation? > > My purpose is to analyze a signal via simulation so as to determine > the compliance of its PSD to a regulatory mask. I am using the term > "dynamic range" informally to refer to how far down in the stopband > the artifact of the window is. > > A Dolph-Chebyshev window with -100 dB sidelobes did not, on first attempt, > give a lower artifact than the Nuttall-Blackman window I have been > using. > > I have the results I need for the requirement at hand, but I'm generally > interested in learning if there's a good way of doing what I'm trying > to do, that can resolve to -80 dBc or so in the stopband. > > Steve >Steve, OK, well I tend to categorize windows like this: - Narrowest possible main lobe in order to have the greatest selectivity or ability to separate nearby sources. Unless you go crazy with sidelobe levels there isn't much to be done with this. - Lowest possible side lobes (usually consistent with main lobe width). This means minimax and they are all equal while being the lowest possible. One would use this if there were *no* knowledge of the "interfering" sources. - Fast decaying sidelobes. One would use this if the interfering sources are likely well removed from the main lobe. That way, you get the benefit of the decay and lower sidelobes "out there" compared to minimax. - Forced-zero sidelobes. One would use this if the interfering sources are at fixed point(s). Could be simulated with a minimax program and exceptionally high weights for short spans. That is stopband1 (normal), stopband2(high weight like 10^3 greater, close to zero), stopband3(normal) all contiguous.... that sort of thing. Your spec's confuse me a bit. You talk about "resolving in the stop band". I don't know what that is. So, there may be a disconnect. In fact, I wouldn't generally use "stop band" in the context of a window function - but I guess I know what you mean: the sidelobe region in the Fourier Transform of the window. (?) I don't know what "artifact of the window" means either..... I guess it could mean something like this: "I want to measure the energy of a distorted sine wave at its fundamental frequency. To the extent that distortion lines have sidelobes themselves, to what extent will the distortion be measured as part of the fundamental *at* the fundamental frequency?" and, vice versa, if one is analyzing the energy of a distortion line / harmonic that would be perturbed by the fundamental or other harmonics. I can imagine wanting to supress signals in the the sidelobe region - meaning to have low sidelobes. I take that to mean your "stopband". So, I'm trying to help but I'm not sure I'm on point here yet. Fred
Reply by ●October 24, 20102010-10-24
Fred Marshall <fmarshall_xremove_the_xs@xacm.org> wrote:>On 10/23/2010 1:17 PM, Steve Pope wrote:>> My purpose is to analyze a signal via simulation so as to determine >> the compliance of its PSD to a regulatory mask. I am using the term >> "dynamic range" informally to refer to how far down in the stopband >> the artifact of the window is.>> A Dolph-Chebyshev window with -100 dB sidelobes did not, on first attempt, >> give a lower artifact than the Nuttall-Blackman window I have been >> using.>OK, well I tend to categorize windows like this: > >- Narrowest possible main lobe in order to have the greatest selectivity >or ability to separate nearby sources. Unless you go crazy with >sidelobe levels there isn't much to be done with this. > >- Lowest possible side lobes (usually consistent with main lobe width). > This means minimax and they are all equal while being the lowest >possible. One would use this if there were *no* knowledge of the >"interfering" sources. > >- Fast decaying sidelobes. One would use this if the interfering >sources are likely well removed from the main lobe. That way, you get >the benefit of the decay and lower sidelobes "out there" compared to >minimax. > >- Forced-zero sidelobes. One would use this if the interfering sources >are at fixed point(s). Could be simulated with a minimax program and >exceptionally high weights for short spans. That is stopband1 (normal), >stopband2(high weight like 10^3 greater, close to zero), >stopband3(normal) all contiguous.... that sort of thing. > >Your spec's confuse me a bit. You talk about "resolving in the stop >band". I don't know what that is. So, there may be a disconnect. In >fact, I wouldn't generally use "stop band" in the context of a window >function - but I guess I know what you mean: the sidelobe region in the >Fourier Transform of the window. (?)Actually, the concept of "passband" and "stopband" are attributes of the signal of interest, not of the window. However I am using a window (as part of computing PSD, since one cannot compute a PSD without using some sort of window or averaging method, but that is another debate) to analyze these characteristics of a particular type of signal.>I don't know what "artifact of the window" means either.....All spectral estimates will be imperfect in some respect, because they must use a window and any window you pick will have some interaction with the signal of interest and the desired observables. When these imperfections prevent observation of the desired observables, they are "artifacts". Again, this is just terminology.>So, I'm trying to help but I'm not sure I'm on point here yet.No, you're completely on point. Tangent: Dale, in his presentation, uses the concept of "bins". In computing a PSD there is no concept of a bin, since there are no discrete transforms used in a PSD calculation. I think Dale's bins are frequency increments of (1 / (window length)) but I'm not certain this is precisely what is meant. Steve
Reply by ●October 25, 20102010-10-25
On 10/24/2010 1:53 PM, Steve Pope wrote:> Fred Marshall<fmarshall_xremove_the_xs@xacm.org> wrote: > >> On 10/23/2010 1:17 PM, Steve Pope wrote: > >>> My purpose is to analyze a signal via simulation so as to determine >>> the compliance of its PSD to a regulatory mask. I am using the term >>> "dynamic range" informally to refer to how far down in the stopband >>> the artifact of the window is. > >>> A Dolph-Chebyshev window with -100 dB sidelobes did not, on first attempt, >>> give a lower artifact than the Nuttall-Blackman window I have been >>> using. > >> OK, well I tend to categorize windows like this: >> >> - Narrowest possible main lobe in order to have the greatest selectivity >> or ability to separate nearby sources. Unless you go crazy with >> sidelobe levels there isn't much to be done with this. >> >> - Lowest possible side lobes (usually consistent with main lobe width). >> This means minimax and they are all equal while being the lowest >> possible. One would use this if there were *no* knowledge of the >> "interfering" sources. >> >> - Fast decaying sidelobes. One would use this if the interfering >> sources are likely well removed from the main lobe. That way, you get >> the benefit of the decay and lower sidelobes "out there" compared to >> minimax. >> >> - Forced-zero sidelobes. One would use this if the interfering sources >> are at fixed point(s). Could be simulated with a minimax program and >> exceptionally high weights for short spans. That is stopband1 (normal), >> stopband2(high weight like 10^3 greater, close to zero), >> stopband3(normal) all contiguous.... that sort of thing. >> >> Your spec's confuse me a bit. You talk about "resolving in the stop >> band". I don't know what that is. So, there may be a disconnect. In >> fact, I wouldn't generally use "stop band" in the context of a window >> function - but I guess I know what you mean: the sidelobe region in the >> Fourier Transform of the window. (?) > > Actually, the concept of "passband" and "stopband" are attributes > of the signal of interest, not of the window. However I am using > a window (as part of computing PSD, since one cannot compute a PSD > without using some sort of window or averaging method, but that is > another debate) to analyze these characteristics of a particular > type of signal. > >> I don't know what "artifact of the window" means either..... > > All spectral estimates will be imperfect in some respect, because > they must use a window and any window you pick will have some interaction > with the signal of interest and the desired observables. When these > imperfections prevent observation of the desired observables, they > are "artifacts". > > Again, this is just terminology. > >> So, I'm trying to help but I'm not sure I'm on point here yet. > > No, you're completely on point. > > Tangent: Dale, in his presentation, uses the concept of "bins". > In computing a PSD there is no concept of a bin, since there are > no discrete transforms used in a PSD calculation. > > I think Dale's bins are frequency increments of (1 / (window length)) but > I'm not certain this is precisely what is meant. > > > SteveSteve, OK. Well then I think you have to select the window length and shape according to your needs. The longer the window, the narrower the main lobe. Then, the shape affects the finer width of the main lobe (rectangular shape goes with minimum width) so that nonrectangular windows widen the main lobe. Regarding length / maiin lobe width: - If the length is too long then you might split up energy in the signal "passband" or center frequency region. - If the length is too short then you might not be able to differentiate between adjacent components that are harmonics, etc. Regarding sidelobes: - well I pretty much dealt with that earlier, eh? A Dolph-Chebyshev window uses a minimax measure on the sidelobes given the main lobe width. So, it's equiripple in the sidelobes. Nuttall, Blackman, harris, et al aren't equiripple in the sidelobes. The first sidelobes are generally larger (than the optimized Dolph Chebyshev) but there is a decay factor so the sidelobes disappear fairly fast. So, is one better than the other? It depends on your needs. That said, the Dolph-Chebyshev is more an analytical curiosity in my mind. Nice to know about but (I think) seldom used. In some sense having the sidelobes continue forever is an oddity. You can see this in the time domain as higher values at the end of the window. These correspond to a cosine in their transform and it's that cosine that makes those sidelobes be there forever.... Fred
Reply by ●October 25, 20102010-10-25
Fred Marshall <fmarshall_xremove_the_xs@xacm.org> wrote:>On 10/24/2010 1:53 PM, Steve Pope wrote:>OK. Well then I think you have to select the window length and shape >according to your needs.Well, certainly; when performing a PSD, once one has selected the window type, one then selects the window length based on the desired resolution bandwidth. Selecting the length is the less tricky part: the resolution bandwith is proportional to 1 / (window length), and may even be equal to (1 / (window length)) mutliplied by a metric quoted by Dale in his presentatoin (the 3dB bandwith in "bins"). (But I'm trying to better understand this and other metrics in Dale's work.) Ideally, for my purposes, I would have an windowing approach that works well, and for which I could "dial in" the resolution bandwidth over some reasonable range.>A Dolph-Chebyshev window uses a minimax measure on the sidelobes given >the main lobe width. So, it's equiripple in the sidelobes. >Nuttall, Blackman, harris, et al aren't equiripple in the sidelobes. >The first sidelobes are generally larger (than the optimized Dolph >Chebyshev) but there is a decay factor so the sidelobes disappear fairly >fast. >So, is one better than the other? >It depends on your needs.In my case I probably could use something very much like a Nuttall, but which decays even faster.>That said, the Dolph-Chebyshev is more an analytical curiosity in my >mind. Nice to know about but (I think) seldom used. In some sense >having the sidelobes continue forever is an oddity. You can see this in >the time domain as higher values at the end of the window. These >correspond to a cosine in their transform and it's that cosine that >makes those sidelobes be there forever.... > >Fred > >Steve
