| Author |
Message |
kiki
Guest
|
 Posted:
Sun Dec 26, 2004 7:57 am Post subject:
do you have a simple way of roughly estimate the max frequen |
|
|
Hi all,
Do you have a simple way of "roughly" estimate the max freuqency in a plot
of data?
For example, suppse I have collect a trace of data about one week's raining
amount... I have to decide how much is the Nyquist sampling rate and how
many samples do I need... how do I estimate the max frequency in the
rainning data roughly?
If I used Matlab to do data spectrum plot of the past a few years and find
the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist
rate to be 2 cycle per day, i.e. I measure twice data a day... of the
function x(t)...
But now I want to measure once a day, but sampling both x(t) and x'(t)
(derivitative) once per day... for what kind of x(t) can I do this kind of
lazy measurement sampling?
How do I reconstruct the original function x(t) by having the x(t) and x'(t)
samples for one measurement per day?
Can I reduce the measurements to once per week, by sampling x(t), x'(t) ,
x''(t), ... till the 14th derivative?
What are the reasons why this sampling/interpolation scheme has not been
used in practice?
Any ideas?
Thanks a lot, |
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|
 |
Kafir
Guest
|
| Posted:
Sun Dec 26, 2004 7:57 am Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
"kiki" <lunaliu3@yahoo.com> wrote in message
news:cqlenk$bef$1@news.Stanford.EDU...
| Quote: | Hi all,
Do you have a simple way of "roughly" estimate the max freuqency in a plot
of data?
For example, suppse I have collect a trace of data about one week's
raining
amount... I have to decide how much is the Nyquist sampling rate and how
many samples do I need... how do I estimate the max frequency in the
rainning data roughly?
If I used Matlab to do data spectrum plot of the past a few years and find
the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist
rate to be 2 cycle per day, i.e. I measure twice data a day... of the
function x(t)...
But now I want to measure once a day, but sampling both x(t) and x'(t)
(derivitative) once per day... for what kind of x(t) can I do this kind of
lazy measurement sampling?
|
it is less than Nyquist, so you have distorted data
| Quote: |
How do I reconstruct the original function x(t) by having the x(t) and
x'(t)
samples for one measurement per day?
Can I reduce the measurements to once per week, by sampling x(t), x'(t) ,
x''(t), ... till the 14th derivative?
What are the reasons why this sampling/interpolation scheme has not been
used in practice?
|
Think of it, using only one sample per week, you can predict the rain amouts
for each day?
hardly.
derivitatives bring up "noise", by the second/third your data is all noise
a derivitative is a high pass filter
| Quote: | Any ideas?
Thanks a lot,
|
|
|
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|
|
Franz Heymann
Guest
|
| Posted:
Sun Dec 26, 2004 11:09 am Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
"kiki" <lunaliu3@yahoo.com> wrote in message
news:cqlenk$bef$1@news.Stanford.EDU...
| Quote: | Hi all,
Do you have a simple way of "roughly" estimate the max freuqency in
a plot
of data?
|
Double the rciprocal of the mean time between observations is a
reasonable figure to use.
Franz |
|
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|
|
Jerry Avins
Guest
|
| Posted:
Sun Dec 26, 2004 8:50 pm Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
kiki wrote:
| Quote: | Hi all,
Do you have a simple way of "roughly" estimate the max freuqency in a plot
of data?
For example, suppse I have collect a trace of data about one week's raining
amount... I have to decide how much is the Nyquist sampling rate and how
many samples do I need... how do I estimate the max frequency in the
rainning data roughly?
If I used Matlab to do data spectrum plot of the past a few years and find
the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist
rate to be 2 cycle per day, i.e. I measure twice data a day... of the
function x(t)...
But now I want to measure once a day, but sampling both x(t) and x'(t)
(derivitative) once per day... for what kind of x(t) can I do this kind of
lazy measurement sampling?
How do I reconstruct the original function x(t) by having the x(t) and x'(t)
samples for one measurement per day?
Can I reduce the measurements to once per week, by sampling x(t), x'(t) ,
x''(t), ... till the 14th derivative?
What are the reasons why this sampling/interpolation scheme has not been
used in practice?
Any ideas?
Thanks a lot,
|
You can always find a way to push a system beyond it's applicable domain
by ignoring the details needed to get it there. I'll go you one (or two)
better.
You can't sample rainfall at all because at any instant there's either a
drop or there isn't, and sampling is about what happens at instants.
When a drop hits, the derivative is, at the very least, very large, and
between drops, it is zero. So sampling the derivative isn't much use.
OK: lets get real. What we really do ...
Wait: you tell me. How do you propose to collect your samples? What
limitations do that sampling scheme impose? When you respect those
limitations, is there still a dilemma?
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Tim Wescott
Guest
|
| Posted:
Sun Dec 26, 2004 9:52 pm Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
kiki wrote:
| Quote: | Hi all,
Do you have a simple way of "roughly" estimate the max freuqency in a plot
of data?
For example, suppse I have collect a trace of data about one week's raining
amount... I have to decide how much is the Nyquist sampling rate and how
many samples do I need... how do I estimate the max frequency in the
rainning data roughly?
|
How did you collect the data in a way that you're sure you haven't
already introduced sampling error?
| Quote: |
If I used Matlab to do data spectrum plot of the past a few years and find
the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist
rate to be 2 cycle per day, i.e. I measure twice data a day... of the
function x(t)...
|
You obviously aren't measuring rain in western Oregon.
| Quote: |
But now I want to measure once a day, but sampling both x(t) and x'(t)
(derivitative) once per day... for what kind of x(t) can I do this kind of
lazy measurement sampling?
|
In theory any x(t) for which two measurements per day would be adequate
-- that means an x(t) which is _strictly_ bandlimited.
| Quote: |
How do I reconstruct the original function x(t) by having the x(t) and x'(t)
samples for one measurement per day?
|
I don't know offhand, so offhand I'd say you actually do some math
before you ask the question. Then you'll not only know the answer,
you'll also understand it. Start with the fact that x(t) is strictly
bandlimited, and remember that the Taylor's series expansion figures in
there somehow.
| Quote: |
Can I reduce the measurements to once per week, by sampling x(t), x'(t) ,
x''(t), ... till the 14th derivative?
|
Sure -- if you are getting _really good_ derivatives, and if your x(t)
is really truly bandlimited. Of course, if you want to get really good
estimates of the derivatives from observation and you're not sure about
the bandlimiting of x(t) then you need to sample it twice each day...
| Quote: |
What are the reasons why this sampling/interpolation scheme has not been
used in practice?
|
Think about it using _your own brain_ and you'll not only know the
answer, but you'll also understand it.
| Quote: |
Any ideas?
Thanks a lot,
Kiki, get out of Matlab, turn off your computer, get out of the lab, go |
outside, stare at the sky and THINK for a while, will you?
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com |
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Y.Porat
Guest
|
| Posted:
Mon Dec 27, 2004 9:47 pm Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
Have you a way to estimate the
lowest em wave possible frequency -in general
not just in a private case??
TIA
Y.Porat
------------------------ |
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jim
Guest
|
| Posted:
Tue Dec 28, 2004 2:14 am Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
Jerry Avins wrote:
| Quote: |
You can't sample rainfall at all because at any instant there's either a
drop or there isn't, and sampling is about what happens at instants.
|
I would disagree. When a farmer wants to know how much rainfall there
has been in order to decide how much irrigation his crops will require
he has a perfectly good bandlimited continuous function called
'rainfall' which he can refer to. And it is indeed a function that is
sampled at instants (points in both time and space) even though the
sampling device may spend all 24/7 collecting data. Also, it is a very
accurate representation of the moisture that is getting to the roots of
his crops which is what the farmer means when he says 'rainfall'.
| Quote: | When a drop hits, the derivative is, at the very least, very large, and
between drops, it is zero. So sampling the derivative isn't much use.
|
2 rain gauges set a foot apart in the open will have no discernible
difference in their readings so there is no need to measure individual
raindrops. The diameter of the rain gauge (within reason) has no effect
on the measurement of the rainfall function - the function just simply
isn't changing fast enough.
What you or the OP mean by measuring the derivatives of rainfall I have
no clue.
-jim
| Quote: | OK: lets get real. What we really do ...
Wait: you tell me. How do you propose to collect your samples? What
limitations do that sampling scheme impose? When you respect those
limitations, is there still a dilemma?
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ
|
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Jerry Avins
Guest
|
| Posted:
Tue Dec 28, 2004 4:03 am Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
jim wrote:
| Quote: |
Jerry Avins wrote:
You can't sample rainfall at all because at any instant there's either a
drop or there isn't, and sampling is about what happens at instants.
I would disagree. When a farmer wants to know how much rainfall there
has been in order to decide how much irrigation his crops will require
he has a perfectly good bandlimited continuous function called
'rainfall' which he can refer to. And it is indeed a function that is
sampled at instants (points in both time and space) even though the
sampling device may spend all 24/7 collecting data. Also, it is a very
accurate representation of the moisture that is getting to the roots of
his crops which is what the farmer means when he says 'rainfall'.
|
He doesn't sample the rate of fall at an instant in time. Instead, he
checks his rain gauge for accumulated rainfall. He is rarely interested
in rate, and when he is, he settles for an average rate over some
(probably variable) time.
| Quote: | When a drop hits, the derivative is, at the very least, very large, and
between drops, it is zero. So sampling the derivative isn't much use.
2 rain gauges set a foot apart in the open will have no discernible
difference in their readings so there is no need to measure individual
raindrops. The diameter of the rain gauge (within reason) has no effect
on the measurement of the rainfall function - the function just simply
isn't changing fast enough.
What you or the OP mean by measuring the derivatives of rainfall I have
no clue.
|
In most places, an inch an hour is considered heavy rain, but it
frequently rains at that heavy rate for brief periods. Once, when it had
already rained copiously during much of the day, we had a total
additional rainfall of 4 inches in a little under an hour. Children used
inflatable wading pools to raft down our main street. The manhole cover
at it low point had been pushed aside by the water pressure and a geyser
of much diluted sewage spewed 12 feet into the air. Although usually
only the total matters, sometimes rate matters too.
The OP's error was treating rainfall as a bandlimited periodic function.
I was trying to get him to think instead of just pushing variables
around. Similar problems arise when sampling stock prices.
...
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Ronald H. Nicholson Jr.
Guest
|
| Posted:
Tue Dec 28, 2004 4:59 pm Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
In article <3384ukF3rpa1gU1@individual.net>, Jerry Avins <jya@ieee.org> wrote:
| Quote: | You can't sample rainfall at all because at any instant there's either a
drop or there isn't, and sampling is about what happens at instants.
When a drop hits, the derivative is, at the very least, very large, and
between drops, it is zero. So sampling the derivative isn't much use.
|
On any of the visual rain gauge I've used, a single rain drop would not
register above measurement error (noise). Fortunately, a rain gauge is
an integrator, so one can just wait long enough to see about how long
it takes for the change in measurement to become perceptible, and then
use the reciprocal to get the derivative within your measurement error
bounds.
The derivative is quite important in terms of choice of clothing and/or
rain gear. An inch of downpour in 10 minutes will have quite a different
effect on ones comfort outdoors compared an inch of sprinkles spread
roughly evenly over 24 hours (other environmental conditions being
equal). Due to evaporation effects and the possibility of damage to
blossoms, this rate makes a difference to farmers as well.
Stock price reports are weird because they usually report the closing
price, instead of the daily or running average. There's no integration
or low pass filter on the number stream (other than that indirectly
caused by human nature and trading strategies).
IMHO. YMMV.
--
Ron Nicholson rhn AT nicholson DOT com http://www.nicholson.com/rhn/
#include <canonical.disclaimer> // only my own opinions, etc. |
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jim
Guest
|
| Posted:
Tue Dec 28, 2004 7:55 pm Post subject:
Re: do you have a simple way of roughly estimate the max fr |
|
|
Jerry Avins wrote:
| Quote: |
The OP's error was treating rainfall as a bandlimited periodic function.
|
Your error is you have said nothing to support this claim. If the
farmers fields are flat his definition of rainfall is in fact a
bandlimited periodic function and he's not to terribly interested in
what effect it has on your pavement covered environment.
If your interested in examining rainfall on a cyclic period of 5 to 10
days it doesn't much matter whether you collect data religiously once an
hour or once a day your conclusions based on the data on whether to
irrigate (to artificially maintain the optimal periodic cycle) will be
the same.
-jim
| Quote: | I was trying to get him to think instead of just pushing variables
around. Similar problems arise when sampling stock prices.
...
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ
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Fred Marshall
Guest
|
| Posted:
Tue Dec 28, 2004 8:57 pm Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message
news:cqm650$dom$3@titan.btinternet.com...
| Quote: |
"kiki" <lunaliu3@yahoo.com> wrote in message
news:cqlenk$bef$1@news.Stanford.EDU...
Hi all,
Do you have a simple way of "roughly" estimate the max freuqency in
a plot
of data?
Double the rciprocal of the mean time between observations is a
reasonable figure to use.
Franz
|
???? If an "observation" is a "sample" then how does this address the
concern?
Fred |
|
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|
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Fred Marshall
Guest
|
| Posted:
Tue Dec 28, 2004 9:08 pm Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
Some suggestions below:
Fred
"kiki" <lunaliu3@yahoo.com> wrote in message
news:cqlenk$bef$1@news.Stanford.EDU...
| Quote: | Hi all,
Do you have a simple way of "roughly" estimate the max freuqency in a plot
of data?
For example, suppse I have collect a trace of data about one week's
raining amount... I have to decide how much is the Nyquist sampling rate
and how many samples do I need... how do I estimate the max frequency in
the rainning data roughly?
|
You could compute a Fourier Transform of the data. That would probably mean
computing an FFT using a very high sample rate.
Under the assumption that you're using a rainfall guage, it integrates the
individual drops and even some of the small squalls. So, the individual
raindrops are not the issue here.
| Quote: |
If I used Matlab to do data spectrum plot of the past a few years and find
the spectrum is between -1 to 1 cycle per day... so I decide the Nyquist
rate to be 2 cycle per day, i.e. I measure twice data a day... of the
function x(t)...
|
How often was the data sampled in the first place?
What is a "cycle" in this context? I don't know what "-1 cycle" means -
that the rain was falling up?
| Quote: | But now I want to measure once a day, but sampling both x(t) and x'(t)
(derivitative) once per day... for what kind of x(t) can I do this kind of
lazy measurement sampling?
|
What is x(t)? What was measured? Is it a rainfall guage?
| Quote: |
How do I reconstruct the original function x(t) by having the x(t) and
x'(t) samples for one measurement per day?
|
It probably isn't too much of a stretch to say: "you can't"
| Quote: |
Can I reduce the measurements to once per week, by sampling x(t), x'(t) ,
x''(t), ... till the 14th derivative?
What are the reasons why this sampling/interpolation scheme has not been
used in practice?
|
If you have a function that is nicely defined mathematically, then in theory
you might be able to do this. In that case you'd be using a mathematical
manipulation to go from one set of numbers to another. Maybe that's properly
called a mapping.
However, in the real world you don't have such a nice math function and
using the derivatives don't work for a number of reasons. One of those
reasons is that the underlying "data" is from a random process. Another is
that there is likely noise in real data - which adds more randomness. |
|
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|
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Guest
|
| Posted:
Tue Dec 28, 2004 11:28 pm Post subject:
Re: do you have a simple way of roughly estimate the max fr |
|
|
Can you stop re-arranging the letters and spacings in the subject line
of these posts. It's a little disorientating to have a thread
breaking off into several permutations within the group It's makes a
mess in Google as well.
jim <"N0sp"@m.sjedging@mwt.net> wrote:
| Quote: |
Jerry Avins wrote:
The OP's error was treating rainfall as a bandlimited periodic function.
Your error is you have said nothing to support this claim. If the
farmers fields are flat his definition of rainfall is in fact a
bandlimited periodic function and he's not to terribly interested in
what effect it has on your pavement covered environment.
If your interested in examining rainfall on a cyclic period of 5 to 10
days it doesn't much matter whether you collect data religiously once an
hour or once a day your conclusions based on the data on whether to
irrigate (to artificially maintain the optimal periodic cycle) will be
the same.
-jim
I was trying to get him to think instead of just pushing variables
around. Similar problems arise when sampling stock prices.
...
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ
----== Posted via Newsfeeds.Com - Unlimited-Uncensored-Secure Usenet News==----
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Jerry Avins
Guest
|
| Posted:
Wed Dec 29, 2004 3:04 am Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
Ronald H. Nicholson Jr. wrote:
| Quote: | In article <3384ukF3rpa1gU1@individual.net>, Jerry Avins <jya@ieee.org> wrote:
You can't sample rainfall at all because at any instant there's either a
drop or there isn't, and sampling is about what happens at instants.
When a drop hits, the derivative is, at the very least, very large, and
between drops, it is zero. So sampling the derivative isn't much use.
On any of the visual rain gauge I've used, a single rain drop would not
register above measurement error (noise). Fortunately, a rain gauge is
an integrator, so one can just wait long enough to see about how long
it takes for the change in measurement to become perceptible, and then
use the reciprocal to get the derivative within your measurement error
bounds.
The derivative is quite important in terms of choice of clothing and/or
rain gear. An inch of downpour in 10 minutes will have quite a different
effect on ones comfort outdoors compared an inch of sprinkles spread
roughly evenly over 24 hours (other environmental conditions being
equal). Due to evaporation effects and the possibility of damage to
blossoms, this rate makes a difference to farmers as well.
Stock price reports are weird because they usually report the closing
price, instead of the daily or running average. There's no integration
or low pass filter on the number stream (other than that indirectly
caused by human nature and trading strategies).
IMHO. YMMV.
|
The OP was trying to treat rainfall as a continuous function with
measurable derivatives of all orders. My ridiculous counter example was
intended to remind him that not every theory of measurement can be
applied to every measurement. You know better, so my scenario wasn't
intended for you (or others who also don't need to be reminded).
The weather bureau's reporting of average temperatures is also weird.
The report not the integrated average, but the arithmetic mean of high
and low. So a that starts with 30 degrees and rising at midnight,
reaches a high of 60 before noon and stays around there until dark,
falling to 45 by midnight has an average temperature of 40 degrees. A
day that starts at 40, drops to 30 by morning, rises slightly to 35 by
noon, briefly reaches 60 by late afternoon, then quickly descends,
reaching 30 again by midnight, has the same average.
Both stock prices and daily average temperatures are sampled once daily.
Can they be considered to be bandlimited to 1/2 cycle per day, or are
they aliased? How would aliasing be manifest?
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
|
| Posted:
Wed Dec 29, 2004 3:07 am Post subject:
Re: do you have a simple way of roughly estimate the max fre |
|
|
Fred Marshall wrote:
...
| Quote: | If you have a function that is nicely defined mathematically, then in theory
you might be able to do this. In that case you'd be using a mathematical
manipulation to go from one set of numbers to another. Maybe that's properly
called a mapping.
However, in the real world you don't have such a nice math function and
using the derivatives don't work for a number of reasons. One of those
reasons is that the underlying "data" is from a random process. Another is
that there is likely noise in real data - which adds more randomness.
|
Aw, Fred! You let out the secret!
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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