1. Offtopic - sampling problem
Hi All,
I am trying to solve a sampling problem and I have simplified it as
below.
Imagine this set contains precisely accurate real-world data that we
wish to record into
the computer (could be temperature or anything)
1, 4, 2, 6, 5, 7, 3, 9, 4
Now, suppose we tried to capture each iteration with a sampling system
that was not
focussed narrowly enough and so each sampled value acquired contained
some overlap
from each adjacent value, assuming a spread of 25%, 50%, 25% we would
get:
1.5, 2.75, 3.5, 4.75, 5.75, 5.5, 5.5, 6.25, 4.25
Each captured value tends to get "smeared" toward the average value
My Question is this: Does anyone know of or could point to a way to
focus
the 2nd sample set back to the original set?
Any help on this is really appreciated.
Yours truly
Mike
vulcan at win.co.nz
2. Re: Offtopic - sampling problem
- Posted by rforno at tutopia.com
Jan 26, 2002
Some sound-processing systems use algorithms to "soften" sound and to
"sharpen" it. I think this is what you need. However:
1) I don't know the algorithms.
2) It seems, according to the results obtained, that "soften" algorithms are
OK, but "sharpen" ones do not work very well (in order to restore the
original signal), due to the fact that some information is lost forever.
----- Original Message -----
From: "Mike" <vulcan at win.co.nz>
To: "EUforum" <EUforum at topica.com>
Subject: Offtopic - sampling problem
>
> Hi All,
>
> I am trying to solve a sampling problem and I have simplified it as
> below.
> Imagine this set contains precisely accurate real-world data that we
> wish to record into
> the computer (could be temperature or anything)
>
> 1, 4, 2, 6, 5, 7, 3, 9, 4
>
> Now, suppose we tried to capture each iteration with a sampling system
> that was not
> focussed narrowly enough and so each sampled value acquired contained
> some overlap
> from each adjacent value, assuming a spread of 25%, 50%, 25% we would
> get:
>
> 1.5, 2.75, 3.5, 4.75, 5.75, 5.5, 5.5, 6.25, 4.25
>
> Each captured value tends to get "smeared" toward the average value
>
> My Question is this: Does anyone know of or could point to a way to
> focus
> the 2nd sample set back to the original set?
>
> Any help on this is really appreciated.
>
> Yours truly
> Mike
> vulcan at win.co.nz
>
>
>
>
3. Re: Offtopic - sampling problem
Mike,
Here's the best I can observe:
let: a b c d e f g h i be the actual original values;
let: A B C D E F G H I be the perceived values;
then:
A = .25x0 + .5a + .25b
B = .25a + .5b + .25c
C = .25b + .5c + .25d
D = .25c + .5d + .25e
E = .25d + .5e + .25f
F = .25e + .5f + .25g
G = .25f + .5g + .25h
H = .25g + .5h + .25i
I = .25h + .5i + .25x0
This is a set of 9 equations in 9 unknowns, which should(?) be solvable.
I suppose you might use matrices to solve them (or just substitution), but
longer sample lengths would probably(?) be prohibitive. If you do have
longer samples, I suppose you could arbitrarily select groups of data of
some size and "throw-away" the values before the beginning & after the end
of each group (call them whatever the average is?), and "solve" each group
separately? Dunno if that's a help or not.
Dan Moyer
----- Original Message -----
From: "Mike" <vulcan at win.co.nz>
To: "EUforum" <EUforum at topica.com>
Sent: Saturday, January 26, 2002 1:09 PM
Subject: Offtopic - sampling problem
>
> Hi All,
>
> I am trying to solve a sampling problem and I have simplified it as
> below.
> Imagine this set contains precisely accurate real-world data that we
> wish to record into
> the computer (could be temperature or anything)
>
> 1, 4, 2, 6, 5, 7, 3, 9, 4
>
> Now, suppose we tried to capture each iteration with a sampling system
> that was not
> focussed narrowly enough and so each sampled value acquired contained
> some overlap
> from each adjacent value, assuming a spread of 25%, 50%, 25% we would
> get:
>
> 1.5, 2.75, 3.5, 4.75, 5.75, 5.5, 5.5, 6.25, 4.25
>
> Each captured value tends to get "smeared" toward the average value
>
> My Question is this: Does anyone know of or could point to a way to
> focus
> the 2nd sample set back to the original set?
>
> Any help on this is really appreciated.
>
> Yours truly
> Mike
> vulcan at win.co.nz
>
>
>
>
4. Re: Offtopic - sampling problem
Mike,
Go to archives, get the simultaneous equations solver by Laurence Draper,
"simul.e"; change the main function "Solve_Simultaneous" to a global
function; then run this modification of his example that has just your
perceived data in it, and it will give you the original actual data:
-- tested code follows:
include simul.e
sequence A --Matrix of coefficients
sequence b --Column vector of results
sequence x --Column vector of solutions
A = {{.5,.25,0,0,0,0,0,0,0},
{.25,.5,.25,0,0,0,0,0,0},
{0,.25,.5,.25,0,0,0,0,0},
{0,0,.25,.5,.25,0,0,0,0},
{0,0,0,.25,.5,.25,0,0,0},
{0,0,0,0,.25,.5,.25,0,0},
{0,0,0,0,0,.25,.5,.25,0},
{0,0,0,0,0,0,.25,.5,.25},
{0,0,0,0,0,0,0,.25,.5}}
b = {1.5, 2.75, 3.5, 4.75, 5.75, 5.5, 5.5, 6.25, 4.25}
if length(A[1]) = length(b) then
dimension = length(A[1])
x = Solve_Simultaneous(A,b)
? x
else
puts(1, "Matrices are incorrect size!!!!")
end if
-- code ends
This will handle your *simplified* example.
Dan Moyer
----- Original Message -----
From: "Mike" <vulcan at win.co.nz>
To: "EUforum" <EUforum at topica.com>
Sent: Saturday, January 26, 2002 1:09 PM
Subject: Offtopic - sampling problem
>
> Hi All,
>
> I am trying to solve a sampling problem and I have simplified it as
> below.
> Imagine this set contains precisely accurate real-world data that we
> wish to record into
> the computer (could be temperature or anything)
>
> 1, 4, 2, 6, 5, 7, 3, 9, 4
>
> Now, suppose we tried to capture each iteration with a sampling system
> that was not
> focussed narrowly enough and so each sampled value acquired contained
> some overlap
> from each adjacent value, assuming a spread of 25%, 50%, 25% we would
> get:
>
> 1.5, 2.75, 3.5, 4.75, 5.75, 5.5, 5.5, 6.25, 4.25
>
> Each captured value tends to get "smeared" toward the average value
>
> My Question is this: Does anyone know of or could point to a way to
> focus
> the 2nd sample set back to the original set?
>
> Any help on this is really appreciated.
>
> Yours truly
> Mike
> vulcan at win.co.nz
>
>
>
>
