Reply by dbd February 8, 20082008-02-08
On Feb 7, 6:37 pm, M.Aram...@verizon.net wrote:
> Different books and papers define the Hamming window with slight > differently coefficients. > Many give the constant term simpy as 0.54. > Some claim that the 0.54 is a rounded off value and the exact value is > 25/46 which is approximately 0.543478261. > Other sources also claim that the 0.54 is a rounded off value, but > that a more precise value is instead 0.53836. > > If the constant term is 25/46, there will be a null in the continous > Fourier transform at alpha=5*pi. > > On the other hand the maximum level of the sidelobes will be lower > with a constant term of 0.53836. > > While there are sometimes practical reasons for approximating numbers > to only a few decimal places in this day and age of hardware floating > point it seems a bit extreme to round off to only two significant > figures. > E.g. except for doing very rough calculations in one's head, I don't > see people using 3.1 as an approximation for pi in serious signal > processing calculations. > However in the case of the Hamming window it could be that 0.54 is > frequently used not because it is round (in decimal notation, at > least), but because it is a compromise value between two values which > are optimal by different criteria. > > -Michael
The rounding to 2 digits was around back in the 1950's at Bell Labs. Blackman and Tukey published the 2 digit rounded forms of Hamming (two coefficient Blackman if you wish) and three coefficient Blackman and the exact rational values required to produce zeros at, in their notation: f = 1.25/T and f = 1.75/T, 2.25/T in their two part article in the Bell System Technical Journal. This was widely available as a Dover reprint. These followed the 2 coefficient von Hann window which was in the form: [1 + cos(...)] / 2 giving no temptation to round. Dale B. Dalrymple
Reply by dbd February 8, 20082008-02-08
On Feb 7, 7:24 pm, robert bristow-johnson <r...@audioimagination.com>
wrote:

>... > > I disagree with your assertion, however, that Hann windows are in the > > same family as Hamming and Blackman. > > just a difference in the coefficients of those four terms: > > 3 > w(t) = SUM{ a[k] * cos(k*pi*t) * rect(t/2) } > k=0
Which is the 4 term or in the frequency domain 7 coefficient set of windows, a subset of the larger set of odd number of coefficient (frequency domain) kernels. Where Von Hann and Hamming are members of the 2 coefficient or 3 term frequency domain subset.
> > in something that i wrote in JAES over a decade ago (and it's also in > that Wavetable Synthesis 101 thingie that is getable from the web), i > proposed the use of one that is > ... > i called it a "Flattened Hann" window. > ... > r b-j
I said every Tom, Dick and Harry had done this. I should have included Robert, too. Dale B. Dalrymple
Reply by Steve Underwood February 8, 20082008-02-08
Jerry Avins wrote:
> Philip Martel wrote: > > ... > >> The formulas appear very similar, why do you consider the Hann window >> to be in a different family? >> http://en.wikipedia.org/wiki/Window_function#Hamming_window > > This is silly. A family is a grouping that contains whatever someone > wants it to. Hoe many cars are touted to have the best mileage, the most > room, the highest resale value, etc. in its class? As far as I know, all > of them. It's all in how the admen define "class". So define "family".
Neat. He worked "ad men" and "class" into the same sentence. :-) Steve
Reply by robert bristow-johnson February 7, 20082008-02-07
On Feb 7, 1:43 pm, Jubilation_T_Cornpone_...@hotmail.com wrote:
> On Feb 6, 9:05 pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote: > > > > > On Wed, 6 Feb 2008 09:26:06 -0800 (PST), > > > Jubilation_T_Cornpone_...@hotmail.com wrote: > > >On Feb 5, 1:38 pm, robert bristow-johnson <r...@audioimagination.com> > > >wrote: > > > >> i'm curious what is meant by "family". would that be different sizes > > >> of the "pedestal" that the Hann part of the Hamming sits upon? > > > >If you hold your mouth just right, you can see that a Hamming window... > > > Hello Jubilation, > > don't be too hard on Robert B-J. He's > > a DSP expert, pure and simple, and he deserves some respect. > > > As for holding our mouths just right, we generally > > hold our mouths in just the right position in which > > to pour beer. > > "Hold your mouth just right" is a Southern expression meaning "To look > at something in just the right way". > > No disrepect or suggestion of anything else intended.
it went way over my head. i'm pretty clueless.
> I disagree with your assertion, however, that Hann windows are in the > same family as Hamming and Blackman.
just a difference in the coefficients of those four terms: 3 w(t) = SUM{ a[k] * cos(k*pi*t) * rect(t/2) } k=0 in something that i wrote in JAES over a decade ago (and it's also in that Wavetable Synthesis 101 thingie that is getable from the web), i proposed the use of one that is a[0] = 1/2 a[1] = 9/16 a[2] = 0 a[3] = -1/16 i called it a "Flattened Hann" window. and i liked it not so much for it's first sidelobe characteristic - the first sidelobe was bigger than anybody that i compared it to, other than rect(t) (not t/2). for purposes of look at something in just the right way, where "right" means as a concatination of two complementary splicing functions, a fade-up followed fade-down function (a[0] had to be 1/2 and all other a[even k] coefs had to be zero). because of that is why the rectagular window (which corresponded to butt splicing, the razor blade is at a right angle to the tape) had to be rect(t) not rect(t/2) which was the rect() that Hamming considered. and, i sure Blackman and Harris were comparing to for reference when comparing specific cases of a "family". hey, it's all the same family, they all be getting along. anyway, it was for aesthetic time-domain purposes that i chose those coefficients (and i make no claim that no one else has, but i don't know another name for this case - it is a frequency domain counterpart to this half-band filter with coefs: h[0] = -1/16 h[1] = 0 h[2] = 9/16 h[3] = 1 h[4] = 9/16 h[5] = 0 h[6] = -1/16 they use this window function (and its complementary HPF), at least conceptually at an elementary level, in wavelets and filter banks for prefect reconstruction. but with the roles of frequency domain and time domain switched around. i'm sure the wavelet people have a name for it, but i don't know what it is. i didn't know about any of this when i wrote those two papers and probably the name for this complementary window function should be the same name for this mathematically equivalent complementary half-band filter used for perfect reconstruction. if someone knows a name for that half-band filter, i would appreciate knowing. i can't find the name the only wavelet/fliter_bank book that i have (Gilbert and Nguyen), but i can find a reference to it as an example and student exercise. r b-j
Reply by Jerry Avins February 7, 20082008-02-07
Philip Martel wrote:

   ...

> The formulas appear very similar, why do you consider the Hann window to be > in a different family? > http://en.wikipedia.org/wiki/Window_function#Hamming_window
This is silly. A family is a grouping that contains whatever someone wants it to. Hoe many cars are touted to have the best mileage, the most room, the highest resale value, etc. in its class? As far as I know, all of them. It's all in how the admen define "class". So define "family". Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;
Reply by February 7, 20082008-02-07
Different books and papers define the Hamming window with slight
differently coefficients.
Many give the constant term simpy as 0.54.
Some claim that the 0.54 is a rounded off value and the exact value is
25/46 which is approximately 0.543478261.
Other sources also claim that the 0.54 is a rounded off value, but
that a more precise value is instead 0.53836.

If the constant term is 25/46, there will be a null in the continous
Fourier transform at alpha=5*pi.

On the other hand the maximum level of the sidelobes will be lower
with a constant term of 0.53836.

While there are sometimes practical reasons for approximating numbers
to only a few decimal places in this day and age of hardware floating
point it seems a bit extreme to round off to only two significant
figures.
E.g. except for doing very rough calculations in one's head, I don't
see people using 3.1 as an approximation for pi in serious signal
processing calculations.
However in the case of the Hamming window it could be that 0.54 is
frequently used not because it is round (in decimal notation, at
least), but because it is a compromise value between two values which
are optimal by different criteria.

-Michael
Reply by Philip Martel February 7, 20082008-02-07
<Jubilation_T_Cornpone_CSA@hotmail.com> wrote in message 
news:1c61c576-4071-4d25-95fa-03948074fa6a@q21g2000hsa.googlegroups.com...
On Feb 6, 9:05 pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:
> On Wed, 6 Feb 2008 09:26:06 -0800 (PST), > > Jubilation_T_Cornpone_...@hotmail.com wrote: > >On Feb 5, 1:38 pm, robert bristow-johnson <r...@audioimagination.com> > >wrote: > > >> i'm curious what is meant by "family". would that be different sizes > >> of the "pedestal" that the Hann part of the Hamming sits upon? > > >If you hold your mouth just right, you can see that a Hamming window... > > Hello Jubilation, > don't be too hard on Robert B-J. He's > a DSP expert, pure and simple, and he deserves some respect. > > As for holding our mouths just right, we generally > hold our mouths in just the right position in which > to pour beer. >
>"Hold your mouth just right" is a Southern expression meaning "To look >at something in just the right way".
>No disrepect or suggestion of anything else intended.
>I disagree with your assertion, however, that Hann windows are in the >same family as Hamming and Blackman.
The formulas appear very similar, why do you consider the Hann window to be in a different family? http://en.wikipedia.org/wiki/Window_function#Hamming_window Best wishes, --Phil Martel
Reply by Philip Martel February 7, 20082008-02-07
"Jerry Avins" <jya@ieee.org> wrote in message 
news:CaqdnUOTyp_ZEzfanZ2dnUVZ_hqdnZ2d@rcn.net...
> Rick Lyons wrote: > > ... > >> Are you a fan of Al Capp? I'll bet that %95 of the guys here do not know >> who Jubilation_T_Cornpone is. >> (Of course, Jerry Avins will know.) >> >> [-Rick-] > > When we fought the Yankees and annihilation was near, > Who was there to lead the charge, that took us safe to the rear? > Why it was Jubilation T. Cornpone. > Old "Toot your own horn pone", > Jubilation T. Cornpone, a man who knew no fear. > > When we almost had 'em but the issue still was in doubt, > Who suggested the retreat that turned it into a rout? > Why it was Jubilation T. Cornpone. > Old "Tattered and Torn Pone", > Jubilation T. Cornpone, he kept us hidin' out. > > With our ammunition gone and faced with utter defeat, > Who was it that burned the crops and left us with nothin' to eat? > Why it wuz Jubilation T. Cornpone. > Old "September Morn-pone", > Jubilation T. Cornpone, the pants blown off his seat. > > Thank you, Ray Charles. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > &#4294967295;
&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295; There are a few more verses here: http://lyricsplayground.com/alpha/songs/j/jubilationtcornponelilabnerthemusical.shtml Best wishes, --Phil Martel
Reply by February 7, 20082008-02-07
On Feb 6, 9:05&#4294967295;pm, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:
> On Wed, 6 Feb 2008 09:26:06 -0800 (PST), > > Jubilation_T_Cornpone_...@hotmail.com wrote: > >On Feb 5, 1:38&#4294967295;pm, robert bristow-johnson <r...@audioimagination.com> > >wrote: > > >> i'm curious what is meant by "family". &#4294967295;would that be different sizes > >> of the "pedestal" that the Hann part of the Hamming sits upon? > > >If you hold your mouth just right, you can see that a Hamming window... > > Hello Jubilation, > &#4294967295; &#4294967295;don't be too hard on Robert B-J. &#4294967295;He's > a DSP expert, pure and simple, and he deserves some respect. > > As for holding our mouths just right, we generally > hold our mouths in just the right position in which > to pour beer. >
"Hold your mouth just right" is a Southern expression meaning "To look at something in just the right way". No disrepect or suggestion of anything else intended. I disagree with your assertion, however, that Hann windows are in the same family as Hamming and Blackman.
Reply by Jerry Avins February 7, 20082008-02-07
Rick Lyons wrote:

   ...

> Are you a fan of Al Capp? I'll bet that %95 of the > guys here do not know who Jubilation_T_Cornpone is. > (Of course, Jerry Avins will know.) > > [-Rick-]
When we fought the Yankees and annihilation was near, Who was there to lead the charge, that took us safe to the rear? Why it was Jubilation T. Cornpone. Old "Toot your own horn pone", Jubilation T. Cornpone, a man who knew no fear. When we almost had 'em but the issue still was in doubt, Who suggested the retreat that turned it into a rout? Why it was Jubilation T. Cornpone. Old "Tattered and Torn Pone", Jubilation T. Cornpone, he kept us hidin' out. With our ammunition gone and faced with utter defeat, Who was it that burned the crops and left us with nothin' to eat? Why it wuz Jubilation T. Cornpone. Old "September Morn-pone", Jubilation T. Cornpone, the pants blown off his seat. Thank you, Ray Charles. Jerry -- Engineering is the art of making what you want from things you can get. &#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;&#4294967295;