Ask a question - edaboard.com
elektroda.net NewsGroups Forum Index - Electronics Design - Quaternions for filters
Jeffery Tomas
Guest
Guest
Fri Feb 03, 2012 10:04 am
We know that most filters have amplitude and phase characteristics that are
represented by a complex function. Does anyone know if Quaternions offer
anything more than the complex numbers for filters, Fourier transform, etc?
Tim Wescott
Guest
Guest
Fri Feb 03, 2012 6:39 pm
On Fri, 03 Feb 2012 03:04:52 -0600, Jeffery Tomas wrote:
Quote:
We know that most filters have amplitude and phase characteristics that
are represented by a complex function. Does anyone know if Quaternions
offer anything more than the complex numbers for filters, Fourier
transform, etc?
are represented by a complex function. Does anyone know if Quaternions
offer anything more than the complex numbers for filters, Fourier
transform, etc?
"Quaternions came from Hamilton after his really good work had been done;
and, though beautifully ingenious, have been an unmixed evil to those who
have touched them in any way, including Clerk Maxwell." â Lord Kelvin,
1892. (from the Wikipedia entry on Quaternions)
If you're attracted to quaternions because of the weirdo math -- back
away slowly until you think no one is looking at you any more, then run
like hell. Or get a PhD in math, and have fun. In general filtering
problems they're totally useless -- complex numbers model signal
processing tasks quite well; there's absolutely nothing that quaternions
can add to that particular mix.
Don't even try to use them until you thoroughly understand them, the
consequences of using them, and the implications of the fact that they
are not commutative. I have used them, in a Kalman filter for a
navigation application, and for that application they were the least of
all the various evils that are available for keeping track of 3D
rotations. But in and of themselves, quaternions offer nothing of use
unless you're working in those self-same 3D rotations, and because of
their character their use is exacting, tedious, mind-bending, and
esoteric.
So -- they're fun stuff if you're a university mathematician and can use
them to attract grant money, they're highly useful (in a sump-pump-to-a-
sewer-worker sort of way) if you're doing 3D graphics or navigational
solutions, and a useless curiosity otherwise.
--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?
Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
HardySpicer
Guest
Guest
Sat Feb 04, 2012 1:08 am
On Feb 3, 10:04 pm, "Jeffery Tomas" <Jeffery_To...@Gmail.com> wrote:
Quote:
We know that most filters have amplitude and phase characteristics that are
represented by a complex function. Does anyone know if Quaternions offer
anything more than the complex numbers for filters, Fourier transform, etc?
represented by a complex function. Does anyone know if Quaternions offer
anything more than the complex numbers for filters, Fourier transform, etc?
No need, two variables, real and imag is all that is needed for elect
eng.
Tim Williams
Guest
Guest
Sat Feb 04, 2012 3:33 am
In addition to the other Tim's comments
, I would add: there isn't much
(anything?) you can do with [hyper]complex numbers that matrices of
sufficient order cannot. For instance, linear algebra on matrices of the
form, IIRC,
[ a b]
z = a + bi --> [-b a]
are indistiguishable from complex numbers (including commutativity and
division -- this matrix is nonsingular (= inverse exists) for (a = b) != 0).
The complex number e^(i*theta) is useful in rotations; the corresponding
matrix is of course:
[ cos theta sin theta]
[-sin theta cos theta]
Corresponding rotations in higher dimensions can be formed by incorporating
this submatrix into a higher dimension's identity matrix. IIRC, this, in
turn, is indistinguishable from quaternions, when using a 4x4 matrix with a
3x3 rotation, which looks something like:
[ trig trig trig 0 ]
[ trig trig trig 0 ]
[ trig trig trig 0 ]
[ 0 0 0 1 ]
(I don't remember or care what the exact trigonometry is..)
IIRC, the equivalent of a three-dimensional rotation holds w constant (in
quaternion-space), hence the 'extra' row and column.
High dimension matrices are very helpful to discrete signal processing.
Multiplication is numerical convolution, so filtering and frequency analysis
are relatively simple. A set of samples of length N looks like a vector; if
you multiply the vector, entry by entry, by different (sampled) sine waves,
representing the Nth sample of the sine wave by the j'th column of a matrix,
and the order of sine wave (fundamental or i'th harmonic) as the row, simply
multiplying this vector of data by the matrix is a Fourier transform. And I
have no proof for it, but evidently, and apparently, this matrix is
self-inverse (that is to say, F{F{f(t)}} = f(t) -- the [normalized] Fourier
transform "un-does" itself; likewise, denoting the Fourier transform matrix
as F, F*F = 1, the NxN identity matrix). So you don't need to generate
anything funny to go from frequency to time domain.
You'd never do this practically, of course; an FFT is O(N*log N) compexity,
while (unoptimized) matrix multiplication is at least O(N^2), and usually
O(N^3). But it's handy for small things, very easy on theory (linear
algebra is very powerful, you can write a simple equation which actually
encapsulates billions of computations), and a good way to get your feet wet
in Matlab/Octave (whose fundamental data type is the matrix).
Tim
--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms
"Jeffery Tomas" <Jeffery_Tomas_at_Gmail.com> wrote in message
news:jgg7vk$98a$1_at_dont-email.me...
Quote:
We know that most filters have amplitude and phase characteristics that
are represented by a complex function. Does anyone know if Quaternions
offer anything more than the complex numbers for filters, Fourier
transform, etc?
are represented by a complex function. Does anyone know if Quaternions
offer anything more than the complex numbers for filters, Fourier
transform, etc?
Jeffery Tomas
Guest
Guest
Sat Feb 04, 2012 8:30 am
There seems to be some real geniuses hear that probably know everything
about Quaternions without ever even passing math 101(not necessarily you
specifically, but the others. No wonder I had them on ignore)
The fact is that Quaternions are useful in some areas that allow one to do
more than complex numbers. Quaternions are very useful in 3D fractals.
1. Quaternions are an extension of the complex numbers. These fools that
think extension are useless should be saying the same thing about complex
numbers too, since, after all, they are just an extension of the reals...
oh, they need to say it about rationales, reals, matrices, integrals, and
just about everything else in mathematics.
2. Quaternions are a subset of matrices. They have additional
properties/constraints that make them behave certain ways. You do point this
out but it's better to think of quaternions in there own right... even if
you don't like them much. This is important and what makes them useful. We
could talk in terms of matrices... but if you want to advocate that then you
should be doing it for the complex numbers too.
3. You are right for the most part about rotations. What makes the Fourier
transform work seems to be the rotational aspect. If you try any arbitrary
pseudo-Eulerian kernel in the Fourier transform you end up with another
Fourier like transform(one that can at least be written as a FT). This made
me wonder how Quaternions would work. They would transform a real signal
into, effectively, R^4. We know that the FT transforms R to R^2. I wonder
what 2 extra dimensions would yield? Again, see the 3D fractals.
http://paulbourke.net/fractals/quatjulia/
(I don't know if it's commonly mentioned about these but any
slice(intersection with a plane) of such a fractal yields a 2D view that is
some view of the complex version.)
Most likely what a quaternion would offer is 2 additional phase relations.
What these relations from an extended FT would represent physically would be
what I am interested in.
Martin Brown
Guest
Guest
Sat Feb 04, 2012 6:10 pm
On 03/02/2012 17:39, Tim Wescott wrote:
Quote:
On Fri, 03 Feb 2012 03:04:52 -0600, Jeffery Tomas wrote:
We know that most filters have amplitude and phase characteristics that
are represented by a complex function. Does anyone know if Quaternions
offer anything more than the complex numbers for filters, Fourier
transform, etc?
"Quaternions came from Hamilton after his really good work had been done;
and, though beautifully ingenious, have been an unmixed evil to those who
have touched them in any way, including Clerk Maxwell." â Lord Kelvin,
1892. (from the Wikipedia entry on Quaternions)
If you're attracted to quaternions because of the weirdo math -- back
away slowly until you think no one is looking at you any more, then run
like hell. Or get a PhD in math, and have fun. In general filtering
problems they're totally useless -- complex numbers model signal
processing tasks quite well; there's absolutely nothing that quaternions
can add to that particular mix.
Don't even try to use them until you thoroughly understand them, the
consequences of using them, and the implications of the fact that they
are not commutative. I have used them, in a Kalman filter for a
navigation application, and for that application they were the least of
all the various evils that are available for keeping track of 3D
rotations. But in and of themselves, quaternions offer nothing of use
unless you're working in those self-same 3D rotations, and because of
their character their use is exacting, tedious, mind-bending, and
esoteric.
So -- they're fun stuff if you're a university mathematician and can use
them to attract grant money, they're highly useful (in a sump-pump-to-a-
sewer-worker sort of way) if you're doing 3D graphics or navigational
solutions, and a useless curiosity otherwise.
We know that most filters have amplitude and phase characteristics that
are represented by a complex function. Does anyone know if Quaternions
offer anything more than the complex numbers for filters, Fourier
transform, etc?
"Quaternions came from Hamilton after his really good work had been done;
and, though beautifully ingenious, have been an unmixed evil to those who
have touched them in any way, including Clerk Maxwell." â Lord Kelvin,
1892. (from the Wikipedia entry on Quaternions)
If you're attracted to quaternions because of the weirdo math -- back
away slowly until you think no one is looking at you any more, then run
like hell. Or get a PhD in math, and have fun. In general filtering
problems they're totally useless -- complex numbers model signal
processing tasks quite well; there's absolutely nothing that quaternions
can add to that particular mix.
Don't even try to use them until you thoroughly understand them, the
consequences of using them, and the implications of the fact that they
are not commutative. I have used them, in a Kalman filter for a
navigation application, and for that application they were the least of
all the various evils that are available for keeping track of 3D
rotations. But in and of themselves, quaternions offer nothing of use
unless you're working in those self-same 3D rotations, and because of
their character their use is exacting, tedious, mind-bending, and
esoteric.
So -- they're fun stuff if you're a university mathematician and can use
them to attract grant money, they're highly useful (in a sump-pump-to-a-
sewer-worker sort of way) if you're doing 3D graphics or navigational
solutions, and a useless curiosity otherwise.
I guess you will be even less keen on Clifford Algebras then which are a
superset of all the common number systems and some others.
http://en.wikipedia.org/wiki/Clifford_algebras
I know some physicists who are recasting physics in that notation with
the occasional new insight occurring along the way.
http://www.av8n.com/physics/clifford-intro.htm
(not for the mathematically faint hearted - may cause headaches)
--
Regards,
Martin Brown
Tim Wescott
Guest
Guest
Sat Feb 04, 2012 6:16 pm
On Sat, 04 Feb 2012 17:10:46 +0000, Martin Brown wrote:
Quote:
On 03/02/2012 17:39, Tim Wescott wrote:
On Fri, 03 Feb 2012 03:04:52 -0600, Jeffery Tomas wrote:
We know that most filters have amplitude and phase characteristics
that are represented by a complex function. Does anyone know if
Quaternions offer anything more than the complex numbers for filters,
Fourier transform, etc?
"Quaternions came from Hamilton after his really good work had been
done; and, though beautifully ingenious, have been an unmixed evil to
those who have touched them in any way, including Clerk Maxwell." â
Lord Kelvin, 1892. (from the Wikipedia entry on Quaternions)
If you're attracted to quaternions because of the weirdo math -- back
away slowly until you think no one is looking at you any more, then run
like hell. Or get a PhD in math, and have fun. In general filtering
problems they're totally useless -- complex numbers model signal
processing tasks quite well; there's absolutely nothing that
quaternions can add to that particular mix.
Don't even try to use them until you thoroughly understand them, the
consequences of using them, and the implications of the fact that they
are not commutative. I have used them, in a Kalman filter for a
navigation application, and for that application they were the least of
all the various evils that are available for keeping track of 3D
rotations. But in and of themselves, quaternions offer nothing of use
unless you're working in those self-same 3D rotations, and because of
their character their use is exacting, tedious, mind-bending, and
esoteric.
So -- they're fun stuff if you're a university mathematician and can
use them to attract grant money, they're highly useful (in a
sump-pump-to-a- sewer-worker sort of way) if you're doing 3D graphics
or navigational solutions, and a useless curiosity otherwise.
I guess you will be even less keen on Clifford Algebras then which are a
superset of all the common number systems and some others.
http://en.wikipedia.org/wiki/Clifford_algebras
I know some physicists who are recasting physics in that notation with
the occasional new insight occurring along the way.
http://www.av8n.com/physics/clifford-intro.htm (not for the
mathematically faint hearted - may cause headaches)
On Fri, 03 Feb 2012 03:04:52 -0600, Jeffery Tomas wrote:
We know that most filters have amplitude and phase characteristics
that are represented by a complex function. Does anyone know if
Quaternions offer anything more than the complex numbers for filters,
Fourier transform, etc?
"Quaternions came from Hamilton after his really good work had been
done; and, though beautifully ingenious, have been an unmixed evil to
those who have touched them in any way, including Clerk Maxwell." â
Lord Kelvin, 1892. (from the Wikipedia entry on Quaternions)
If you're attracted to quaternions because of the weirdo math -- back
away slowly until you think no one is looking at you any more, then run
like hell. Or get a PhD in math, and have fun. In general filtering
problems they're totally useless -- complex numbers model signal
processing tasks quite well; there's absolutely nothing that
quaternions can add to that particular mix.
Don't even try to use them until you thoroughly understand them, the
consequences of using them, and the implications of the fact that they
are not commutative. I have used them, in a Kalman filter for a
navigation application, and for that application they were the least of
all the various evils that are available for keeping track of 3D
rotations. But in and of themselves, quaternions offer nothing of use
unless you're working in those self-same 3D rotations, and because of
their character their use is exacting, tedious, mind-bending, and
esoteric.
So -- they're fun stuff if you're a university mathematician and can
use them to attract grant money, they're highly useful (in a
sump-pump-to-a- sewer-worker sort of way) if you're doing 3D graphics
or navigational solutions, and a useless curiosity otherwise.
I guess you will be even less keen on Clifford Algebras then which are a
superset of all the common number systems and some others.
http://en.wikipedia.org/wiki/Clifford_algebras
I know some physicists who are recasting physics in that notation with
the occasional new insight occurring along the way.
http://www.av8n.com/physics/clifford-intro.htm (not for the
mathematically faint hearted - may cause headaches)
OK, I forgot the tie-in with theoretical physics. Oops. Apparently
quaternions describe rotations of particles involved in quantum
electrodynamics fairly well, and octonions work to describe quantum
chromodynamics.
So if you're in love with quaternions you can go for a math _or_ a
physics PhD.
--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?
Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
Tim Wescott
Guest
Guest
Sun Feb 05, 2012 12:18 am
On Sat, 04 Feb 2012 01:30:01 -0600, Jeffery Tomas wrote:
Quote:
There seems to be some real geniuses hear that probably know everything
about Quaternions without ever even passing math 101(not necessarily you
specifically, but the others. No wonder I had them on ignore)
The fact is that Quaternions are useful in some areas that allow one to
do more than complex numbers. Quaternions are very useful in 3D
fractals.
1. Quaternions are an extension of the complex numbers. These fools that
think extension are useless should be saying the same thing about
complex numbers too, since, after all, they are just an extension of the
reals... oh, they need to say it about rationales, reals, matrices,
integrals, and just about everything else in mathematics.
2. Quaternions are a subset of matrices. They have additional
properties/constraints that make them behave certain ways. You do point
this out but it's better to think of quaternions in there own right...
even if you don't like them much. This is important and what makes them
useful. We could talk in terms of matrices... but if you want to
advocate that then you should be doing it for the complex numbers too.
3. You are right for the most part about rotations. What makes the
Fourier transform work seems to be the rotational aspect. If you try any
arbitrary pseudo-Eulerian kernel in the Fourier transform you end up
with another Fourier like transform(one that can at least be written as
a FT). This made me wonder how Quaternions would work. They would
transform a real signal into, effectively, R^4. We know that the FT
transforms R to R^2. I wonder what 2 extra dimensions would yield?
Again, see the 3D fractals.
http://paulbourke.net/fractals/quatjulia/
(I don't know if it's commonly mentioned about these but any
slice(intersection with a plane) of such a fractal yields a 2D view that
is some view of the complex version.)
Most likely what a quaternion would offer is 2 additional phase
relations. What these relations from an extended FT would represent
physically would be what I am interested in.
about Quaternions without ever even passing math 101(not necessarily you
specifically, but the others. No wonder I had them on ignore)
The fact is that Quaternions are useful in some areas that allow one to
do more than complex numbers. Quaternions are very useful in 3D
fractals.
1. Quaternions are an extension of the complex numbers. These fools that
think extension are useless should be saying the same thing about
complex numbers too, since, after all, they are just an extension of the
reals... oh, they need to say it about rationales, reals, matrices,
integrals, and just about everything else in mathematics.
2. Quaternions are a subset of matrices. They have additional
properties/constraints that make them behave certain ways. You do point
this out but it's better to think of quaternions in there own right...
even if you don't like them much. This is important and what makes them
useful. We could talk in terms of matrices... but if you want to
advocate that then you should be doing it for the complex numbers too.
3. You are right for the most part about rotations. What makes the
Fourier transform work seems to be the rotational aspect. If you try any
arbitrary pseudo-Eulerian kernel in the Fourier transform you end up
with another Fourier like transform(one that can at least be written as
a FT). This made me wonder how Quaternions would work. They would
transform a real signal into, effectively, R^4. We know that the FT
transforms R to R^2. I wonder what 2 extra dimensions would yield?
Again, see the 3D fractals.
http://paulbourke.net/fractals/quatjulia/
(I don't know if it's commonly mentioned about these but any
slice(intersection with a plane) of such a fractal yields a 2D view that
is some view of the complex version.)
Most likely what a quaternion would offer is 2 additional phase
relations. What these relations from an extended FT would represent
physically would be what I am interested in.
Oh. You're trolling. I see.
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Jeffery Tomas
Guest
Guest
Sun Feb 05, 2012 12:51 am
"Tim Wescott" wrote in message
news:TL2dndzPiJEuIbDSnZ2dnUVZ_gednZ2d_at_web-ster.com...
On Sat, 04 Feb 2012 01:30:01 -0600, Jeffery Tomas wrote:
Quote:
There seems to be some real geniuses hear that probably know everything
about Quaternions without ever even passing math 101(not necessarily you
specifically, but the others. No wonder I had them on ignore)
The fact is that Quaternions are useful in some areas that allow one to
do more than complex numbers. Quaternions are very useful in 3D
fractals.
1. Quaternions are an extension of the complex numbers. These fools that
think extension are useless should be saying the same thing about
complex numbers too, since, after all, they are just an extension of the
reals... oh, they need to say it about rationales, reals, matrices,
integrals, and just about everything else in mathematics.
2. Quaternions are a subset of matrices. They have additional
properties/constraints that make them behave certain ways. You do point
this out but it's better to think of quaternions in there own right...
even if you don't like them much. This is important and what makes them
useful. We could talk in terms of matrices... but if you want to
advocate that then you should be doing it for the complex numbers too.
3. You are right for the most part about rotations. What makes the
Fourier transform work seems to be the rotational aspect. If you try any
arbitrary pseudo-Eulerian kernel in the Fourier transform you end up
with another Fourier like transform(one that can at least be written as
a FT). This made me wonder how Quaternions would work. They would
transform a real signal into, effectively, R^4. We know that the FT
transforms R to R^2. I wonder what 2 extra dimensions would yield?
Again, see the 3D fractals.
http://paulbourke.net/fractals/quatjulia/
(I don't know if it's commonly mentioned about these but any
slice(intersection with a plane) of such a fractal yields a 2D view that
is some view of the complex version.)
Most likely what a quaternion would offer is 2 additional phase
relations. What these relations from an extended FT would represent
physically would be what I am interested in.
about Quaternions without ever even passing math 101(not necessarily you
specifically, but the others. No wonder I had them on ignore)
The fact is that Quaternions are useful in some areas that allow one to
do more than complex numbers. Quaternions are very useful in 3D
fractals.
1. Quaternions are an extension of the complex numbers. These fools that
think extension are useless should be saying the same thing about
complex numbers too, since, after all, they are just an extension of the
reals... oh, they need to say it about rationales, reals, matrices,
integrals, and just about everything else in mathematics.
2. Quaternions are a subset of matrices. They have additional
properties/constraints that make them behave certain ways. You do point
this out but it's better to think of quaternions in there own right...
even if you don't like them much. This is important and what makes them
useful. We could talk in terms of matrices... but if you want to
advocate that then you should be doing it for the complex numbers too.
3. You are right for the most part about rotations. What makes the
Fourier transform work seems to be the rotational aspect. If you try any
arbitrary pseudo-Eulerian kernel in the Fourier transform you end up
with another Fourier like transform(one that can at least be written as
a FT). This made me wonder how Quaternions would work. They would
transform a real signal into, effectively, R^4. We know that the FT
transforms R to R^2. I wonder what 2 extra dimensions would yield?
Again, see the 3D fractals.
http://paulbourke.net/fractals/quatjulia/
(I don't know if it's commonly mentioned about these but any
slice(intersection with a plane) of such a fractal yields a 2D view that
is some view of the complex version.)
Most likely what a quaternion would offer is 2 additional phase
relations. What these relations from an extended FT would represent
physically would be what I am interested in.
Oh. You're trolling. I see.
-------
Na, just adding another loser to my ignore list... have a nice day!
Jeffery Tomas
Guest
Guest
Sun Feb 05, 2012 12:55 am
"Martin Brown" wrote in message news:nEdXq.8731$rV2.4400_at_newsfe11.iad...
Quote:
On 03/02/2012 17:39, Tim Wescott wrote:
On Fri, 03 Feb 2012 03:04:52 -0600, Jeffery Tomas wrote:
We know that most filters have amplitude and phase characteristics that
are represented by a complex function. Does anyone know if Quaternions
offer anything more than the complex numbers for filters, Fourier
transform, etc?
"Quaternions came from Hamilton after his really good work had been done;
and, though beautifully ingenious, have been an unmixed evil to those who
have touched them in any way, including Clerk Maxwell." â Lord Kelvin,
1892. (from the Wikipedia entry on Quaternions)
If you're attracted to quaternions because of the weirdo math -- back
away slowly until you think no one is looking at you any more, then run
like hell. Or get a PhD in math, and have fun. In general filtering
problems they're totally useless -- complex numbers model signal
processing tasks quite well; there's absolutely nothing that quaternions
can add to that particular mix.
Don't even try to use them until you thoroughly understand them, the
consequences of using them, and the implications of the fact that they
are not commutative. I have used them, in a Kalman filter for a
navigation application, and for that application they were the least of
all the various evils that are available for keeping track of 3D
rotations. But in and of themselves, quaternions offer nothing of use
unless you're working in those self-same 3D rotations, and because of
their character their use is exacting, tedious, mind-bending, and
esoteric.
So -- they're fun stuff if you're a university mathematician and can use
them to attract grant money, they're highly useful (in a sump-pump-to-a-
sewer-worker sort of way) if you're doing 3D graphics or navigational
solutions, and a useless curiosity otherwise.
I guess you will be even less keen on Clifford Algebras then which are a
superset of all the common number systems and some others.
http://en.wikipedia.org/wiki/Clifford_algebras
I know some physicists who are recasting physics in that notation with the
occasional new insight occurring along the way.
http://www.av8n.com/physics/clifford-intro.htm
(not for the mathematically faint hearted - may cause headaches)
Do you seriously think these guys care about anything useful? As long as
they have a calculator that can compute sqrt's and pi they can do all the
math they need(which isn't much). I would doubt they know what an Algebra is
much less a Clifford Algebra.
There responses demonstrate they have no clue about the power of
generalizations. This alone shows there lack of intelligence.
Gib Bogle
Guest
Guest
Sun Feb 05, 2012 1:30 am
On 5/02/2012 12:55 p.m., Jeffery Tomas wrote:
Quote:
Do you seriously think these guys care about anything useful? As long as
they have a calculator that can compute sqrt's and pi they can do all
the math they need(which isn't much). I would doubt they know what an
Algebra is much less a Clifford Algebra.
There responses demonstrate they have no clue about the power of
generalizations. This alone shows there lack of intelligence.
Your use of "there" for "their" doesn't convey a good impression of yours.
Jeffery Tomas
Guest
Guest
Sun Feb 05, 2012 1:34 am
"Gib Bogle" wrote in message news:jgkiiu$hij$2_at_speranza.aioe.org...
Quote:
On 5/02/2012 12:55 p.m., Jeffery Tomas wrote:
Do you seriously think these guys care about anything useful? As long as
they have a calculator that can compute sqrt's and pi they can do all
the math they need(which isn't much). I would doubt they know what an
Algebra is much less a Clifford Algebra.
There responses demonstrate they have no clue about the power of
generalizations. This alone shows there lack of intelligence.
Your use of "there" for "their" doesn't convey a good impression of yours.
I'm not going to play your game of who has the smartest 3rd grade
education... when you graduate 4th grade give me a call and maybe we can
then see who is smarter.
--
Sean_VN
Guest
Guest
Sun Feb 05, 2012 2:01 am
The Walsh Hadamard transform is very fast if you use the right
algorithm. I have done some work on it. www.code.google.com/p/lemontree
John S
Guest
Guest
Mon Feb 06, 2012 2:21 am
On 2/4/2012 6:34 PM, Jeffery Tomas wrote:
Quote:
"Gib Bogle" wrote in message news:jgkiiu$hij$2_at_speranza.aioe.org...
On 5/02/2012 12:55 p.m., Jeffery Tomas wrote:
Do you seriously think these guys care about anything useful? As long as
they have a calculator that can compute sqrt's and pi they can do all
the math they need(which isn't much). I would doubt they know what an
Algebra is much less a Clifford Algebra.
There responses demonstrate they have no clue about the power of
generalizations. This alone shows there lack of intelligence.
Your use of "there" for "their" doesn't convey a good impression of
yours.
I'm not going to play your game of who has the smartest 3rd grade
education... when you graduate 4th grade give me a call and maybe we can
then see who is smarter.
--
On 5/02/2012 12:55 p.m., Jeffery Tomas wrote:
Do you seriously think these guys care about anything useful? As long as
they have a calculator that can compute sqrt's and pi they can do all
the math they need(which isn't much). I would doubt they know what an
Algebra is much less a Clifford Algebra.
There responses demonstrate they have no clue about the power of
generalizations. This alone shows there lack of intelligence.
Your use of "there" for "their" doesn't convey a good impression of
yours.
I'm not going to play your game of who has the smartest 3rd grade
education... when you graduate 4th grade give me a call and maybe we can
then see who is smarter.
--
You will not win.
John S
Guest
Guest
Mon Feb 06, 2012 2:22 am
On 2/4/2012 5:51 PM, Jeffery Tomas wrote:
Quote:
"Tim Wescott" wrote in message
news:TL2dndzPiJEuIbDSnZ2dnUVZ_gednZ2d_at_web-ster.com...
On Sat, 04 Feb 2012 01:30:01 -0600, Jeffery Tomas wrote:
There seems to be some real geniuses hear that probably know everything
about Quaternions without ever even passing math 101(not necessarily you
specifically, but the others. No wonder I had them on ignore)
The fact is that Quaternions are useful in some areas that allow one to
do more than complex numbers. Quaternions are very useful in 3D
fractals.
1. Quaternions are an extension of the complex numbers. These fools that
think extension are useless should be saying the same thing about
complex numbers too, since, after all, they are just an extension of the
reals... oh, they need to say it about rationales, reals, matrices,
integrals, and just about everything else in mathematics.
2. Quaternions are a subset of matrices. They have additional
properties/constraints that make them behave certain ways. You do point
this out but it's better to think of quaternions in there own right...
even if you don't like them much. This is important and what makes them
useful. We could talk in terms of matrices... but if you want to
advocate that then you should be doing it for the complex numbers too.
3. You are right for the most part about rotations. What makes the
Fourier transform work seems to be the rotational aspect. If you try any
arbitrary pseudo-Eulerian kernel in the Fourier transform you end up
with another Fourier like transform(one that can at least be written as
a FT). This made me wonder how Quaternions would work. They would
transform a real signal into, effectively, R^4. We know that the FT
transforms R to R^2. I wonder what 2 extra dimensions would yield?
Again, see the 3D fractals.
http://paulbourke.net/fractals/quatjulia/
(I don't know if it's commonly mentioned about these but any
slice(intersection with a plane) of such a fractal yields a 2D view that
is some view of the complex version.)
Most likely what a quaternion would offer is 2 additional phase
relations. What these relations from an extended FT would represent
physically would be what I am interested in.
Oh. You're trolling. I see.
-------
Na, just adding another loser to my ignore list... have a nice day!
Same here.
elektroda.net NewsGroups Forum Index - Electronics Design - Quaternions for filters
