Most software seems to focus on Hann, Hamming, and Blackman windowing. From the graphs I've seen, Dolph-Chebychev appears to outperform them: https://en.wikipedia.org/wiki/Window_function#Dolph.E2.80.93Chebyshev_window Anyone know why it isn't featured in DSP texts to the extent of the other windows above? Are there drawbacks?
Why is Dolph-Chebychev windowing relatively obscure?
Started by ●March 15, 2017
Reply by ●March 15, 20172017-03-15
On Wednesday, March 15, 2017 at 10:19:41 AM UTC-4, Eric wrote:> Most software seems to focus on Hann, Hamming, and Blackman windowing. > From the graphs I've seen, Dolph-Chebychev appears to outperform them: > https://en.wikipedia.org/wiki/Window_function#Dolph.E2.80.93Chebyshev_window > > Anyone know why it isn't featured in DSP texts to the extent of the > other windows above? Are there drawbacks?wide main lobe. (so when you convolve with it, it's a sloppy transition band.) r b-j
Reply by ●March 15, 20172017-03-15
On Wednesday, March 15, 2017 at 9:19:41 AM UTC-5, Eric wrote:> Anyone know why it isn't featured in DSP texts to the extent of the > other windows above? Are there drawbacks?The equiripple sidelobes look like sinusoids in the frequency domain, which result in impulses in the time domain.
Reply by ●March 15, 20172017-03-15
On Wednesday, March 15, 2017 at 11:54:10 AM UTC-4, Greg Berchin wrote:> On Wednesday, March 15, 2017 at 9:19:41 AM UTC-5, Eric wrote: > > > Anyone know why it isn't featured in DSP texts to the extent of the > > other windows above? Are there drawbacks? > > The equiripple sidelobes look like sinusoids in the frequency domain, which result in impulses in the time domain.ooooh! hadn't known that. that's very similar to using Parks-McClellan to design linear-phase FIRs. lotsa pre-echo and post-echo. r b-j
Reply by ●March 15, 20172017-03-15
> > > > The equiripple sidelobes look like sinusoids in the frequency domain, which result in impulses in the time domain. > >its nuggets of info like that, that make this a great newsgroup thanks Mark
Reply by ●March 15, 20172017-03-15
https://www.dsprelated.com/freebooks/sasp/Dolph_Chebyshev_Window.html; see especially the Length-101 window example.
Reply by ●March 15, 20172017-03-15
On Wed, 15 Mar 2017 13:39:54 -0700 (PDT), Greg Berchin <gjberchin@charter.net> wrote:>https://www.dsprelated.com/freebooks/sasp/Dolph_Chebyshev_Window.html; see especially the Length-101 window example.That's pretty cool. I hadn't thought about that concerning sidelobe ripple before since in most cases the effect in the impulse response is negligible. --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus
Reply by ●March 15, 20172017-03-15
On Wed, 15 Mar 2017 12:02:33 -0700 (PDT), makolber@yahoo.com wrote:> >> > >> > The equiripple sidelobes look like sinusoids in the frequency domain, which result in impulses in the time domain. >> >> > > >its nuggets of info like that, that make this a great newsgroup > >thanks > >MarkNo doubt. Very cool. --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus
Reply by ●March 16, 20172017-03-16
On Wednesday, March 15, 2017 at 1:52:20 PM UTC-7, eric.j...@ieee.org wrote:> ... > > No doubt. Very cool. >Eric The Dolph-Cheb is the narrowest mainlobe for a specified maximun side-lobe height. That makes it sound attractive, but the constraint to hold all side-lobes equal has costs. The side-lobe structure is sensitive to the accuracy of the time delays between samples. When the navy uses towed SONAR arrays, element positioning is not precise, so another solution is used for the spatial window used for beamforming. In the 1950s T. T. Taylor suggested two windows, Taylor(1 parameter), which for historical reasons we now call Kaiser-Bessel (Kaiser better advertised a formula for calculating it in the 1960s)and Taylor(2 parameter) which is used for beamforming. The two parameters are side-lobe rejection (like Dolph-Cheb) and nbar which is the number of sidelobes to keep at constant magnitude before allowing a 6dB per octave roll-off. Sometimes Taylor(2 parameter) is called Taylor-nbar. Taylor-nbar has a mainlobe a few percent wider that Dolph-Cheb and removes the peak at the edgs of the window for most practical applications. Greg Berchins reference to: "https://www.dsprelated.com/freebooks/sasp/Dolph_Chebyshev_Window.html; see especially the Length-101 window example" shows a FIR coefficient set of 101 samples (MATLAB's 'symmetric' version of the window). A spectral analysis version of a -40dB window (MATLAB's 'periodic' or "DFT-even", from the harris paper, window) is show on page 17 of my "Windows Connections" presentation from the 2010 comp.dsp conference: http://www.abvolt.com/compdsp/presentations/Dalrymple/dbd.pdf (And you were there... ) You can get a proper 100 point spectrum analysis window by removing the peak on the right side of the 101 point window in Greg's reference. Dale B. Dalrymple
Reply by ●March 16, 20172017-03-16
On Wed, 15 Mar 2017 21:50:02 -0700 (PDT), dbd <d.dalrymple@sbcglobal.net> wrote:>On Wednesday, March 15, 2017 at 1:52:20 PM UTC-7, eric.j...@ieee.org wrote: >> ... >>=20 >> No doubt. Very cool. >>=20 > >Eric > >The Dolph-Cheb is the narrowest mainlobe for a specified maximun side-lobe = >height. That makes it sound attractive, but the constraint to hold all side= >-lobes equal has costs. The side-lobe structure is sensitive to the accurac= >y of the time delays between samples. When the navy uses towed SONAR arrays= >, element positioning is not precise, so another solution is used for the s= >patial window used for beamforming. > >In the 1950s T. T. Taylor suggested two windows, Taylor(1 parameter), which= > for historical reasons we now call Kaiser-Bessel (Kaiser better advertised= > a formula for calculating it in the 1960s)and Taylor(2 parameter) which is= > used for beamforming. The two parameters are side-lobe rejection (like Dol= >ph-Cheb) and nbar which is the number of sidelobes to keep at constant magn= >itude before allowing a 6dB per octave roll-off. Sometimes Taylor(2 paramet= >er) is called Taylor-nbar. Taylor-nbar has a mainlobe a few percent wider t= >hat Dolph-Cheb and removes the peak at the edgs of the window for most prac= >tical applications. >Taylor's parametric window functions were some of the first I learned way back during my radar days (in the 80s), as they were preferred at the time for SAR processing. I subsequently almost never mention them because it seems like not very many people have heard of them. I've used them here and there when there was benefit to do so, as the parametric adjustments are often useful. Another common window terminology used in radar processing at the time was the "raised cosine" (like a Taylor), which causes confusion with the "raised cosine" pulse shape in communications, and the two don't really have anything to do with each other. So I usually don't speak of the radar window functions. ;)>Greg Berchins reference to: > >"https://www.dsprelated.com/freebooks/sasp/Dolph_Chebyshev_Window.html; >see especially the Length-101 window example" > >shows a FIR coefficient set of 101 samples (MATLAB's 'symmetric' version of= > the window). A spectral analysis version of a -40dB window (MATLAB's 'peri= >odic' or "DFT-even", from the harris paper, window) is show on page 17 of m= >y "Windows Connections" presentation from the 2010 comp.dsp conference: > >http://www.abvolt.com/compdsp/presentations/Dalrymple/dbd.pdf > >(And you were there... )Yeah, I think there's a lot I've forgotten over the years. Not everything sticks, unfortunately. I remember when you presented that that I missed many things because there were a lot of interesting details and I just didn't catch all of them because there were so many. That was probably the deepest dive specifically on windowing/spectral analysis that I've seen.>You can get a proper 100 point spectrum analysis window by removing the pea= >k on the right side of the 101 point window in Greg's reference.Makes sense. This is an interesting reminder how these details can be exploited. --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus
