Thread Subject:

Normalization

I have a data set of time vs. Intensity. Is there quick way to normalize this data set, such that the area under the curve is 1. Perhaps a very stupid question, but any leads are much appreciated.

On Feb 11, 11:20 am, "Desert Hike" <deserth...@gmail.com> wrote:
> I have a data set of time vs. Intensity. Is there quick way to normalize this data set, such that the area under the curve is 1. Perhaps a very stupid question, but any leads are much appreciated.

It's not a stupid question.
What it is is lacking in detail:
1. Are the t equispaced?
2. You say the area is to be unity, but how does that work in terms
of units? e.g., if time is in seconds and intensity is in N/m^2, then
the area will be N-s /m^2. How can that be unity?

TideMan <mulgor@gmail.com> wrote in message <a46ea46e-5c58-4ff2-8833-6fcf91c951d5@d23g2000prj.googlegroups.com>...
> On Feb 11, 11:20 am, "Desert Hike" <deserth...@gmail.com> wrote:
> > I have a data set of time vs. Intensity. Is there quick way to normalize this data set, such that the area under the curve is 1. Perhaps a very stupid question, but any leads are much appreciated.
>
> It's not a stupid question.
> What it is is lacking in detail:
> 1. Are the t equispaced?
> 2. You say the area is to be unity, but how does that work in terms
> of units? e.g., if time is in seconds and intensity is in N/m^2, then
> the area will be N-s /m^2. How can that be unity?

Thanks for your response and apologies for being a bit vague. So basically what I have is a step-response of my instrument (I vs. t). I differentiate this to get an impulse response (dI/dt). Now I want to be able to convolve this impulse response with an arbitrary input to generate the output.
If I normalize the impulse response such that the area under the curve is 1, the the output maintains the same amplitudes as the input (except that now it is convolved).
To answer your specific question:
1. Yes, t is equispaced.
2. For the units: since its the area for the impulse response, so that is (dI/dt)*dt = I should be 1.
Basically, as I said before, I don't know how to quickly implement a code so as to normalise a data-set of x,y values.
Thanks again!

> TideMan <mulgor@gmail.com> wrote in message
> <a46ea46e-5c58-4ff2-8833-6fcf91c951d5@d23g2000prj.goog
> legroups.com>...
> > On Feb 11, 11:20 am, "Desert Hike"
> <deserth...@gmail.com> wrote:
> > > I have a data set of time vs. Intensity. Is there
> quick way to normalize this data set, such that the
> area under the curve is 1. Perhaps a very stupid
> question, but any leads are much appreciated.
> >
> > It's not a stupid question.
> > What it is is lacking in detail:
> > 1. Are the t equispaced?
> > 2. You say the area is to be unity, but how does
> that work in terms
> > of units? e.g., if time is in seconds and
> intensity is in N/m^2, then
> > the area will be N-s /m^2. How can that be unity?
>
> Thanks for your response and apologies for being a
> bit vague. So basically what I have is a
> step-response of my instrument (I vs. t). I
> differentiate this to get an impulse response
> (dI/dt). Now I want to be able to convolve this
> impulse response with an arbitrary input to generate
> the output.
> If I normalize the impulse response such that the
> area under the curve is 1, the the output maintains
> the same amplitudes as the input (except that now it
> is convolved).
> To answer your specific question:
> 1. Yes, t is equispaced.
> 2. For the units: since its the area for the impulse
> response, so that is (dI/dt)*dt = I should be 1.
> Basically, as I said before, I don't know how to
> quickly implement a code so as to normalise a
> data-set of x,y values.
> Thanks again!

ynorm=y./trapz(x,y) ?

Best wishes
Torsten.

Torsten Hennig <Torsten.Hennig@umsicht.fhg.de> wrote in message <1260114039.75890.1297411202212.JavaMail.root@gallium.mathforum.org>...
> > TideMan <mulgor@gmail.com> wrote in message
> > <a46ea46e-5c58-4ff2-8833-6fcf91c951d5@d23g2000prj.goog
> > legroups.com>...
> > > On Feb 11, 11:20 am, "Desert Hike"
> > <deserth...@gmail.com> wrote:
> > > > I have a data set of time vs. Intensity. Is there
> > quick way to normalize this data set, such that the
> > area under the curve is 1. Perhaps a very stupid
> > question, but any leads are much appreciated.
> > >
> > > It's not a stupid question.
> > > What it is is lacking in detail:
> > > 1. Are the t equispaced?
> > > 2. You say the area is to be unity, but how does
> > that work in terms
> > > of units? e.g., if time is in seconds and
> > intensity is in N/m^2, then
> > > the area will be N-s /m^2. How can that be unity?
> >
> > Thanks for your response and apologies for being a
> > bit vague. So basically what I have is a
> > step-response of my instrument (I vs. t). I
> > differentiate this to get an impulse response
> > (dI/dt). Now I want to be able to convolve this
> > impulse response with an arbitrary input to generate
> > the output.
> > If I normalize the impulse response such that the
> > area under the curve is 1, the the output maintains
> > the same amplitudes as the input (except that now it
> > is convolved).
> > To answer your specific question:
> > 1. Yes, t is equispaced.
> > 2. For the units: since its the area for the impulse
> > response, so that is (dI/dt)*dt = I should be 1.
> > Basically, as I said before, I don't know how to
> > quickly implement a code so as to normalise a
> > data-set of x,y values.
> > Thanks again!
>
> ynorm=y./trapz(x,y) ?
>
> Best wishes
> Torsten.


Works! Thanks very much !

"Desert Hike" <deserthike@gmail.com> wrote in message <ij31s0$b96$1@fred.mathworks.com>...
> Torsten Hennig <Torsten.Hennig@umsicht.fhg.de> wrote in message <1260114039.75890.1297411202212.JavaMail.root@gallium.mathforum.org>...
> > > TideMan <mulgor@gmail.com> wrote in message
> > > <a46ea46e-5c58-4ff2-8833-6fcf91c951d5@d23g2000prj.goog
> > > legroups.com>...
> > > > On Feb 11, 11:20 am, "Desert Hike"
> > > <deserth...@gmail.com> wrote:
> > > > > I have a data set of time vs. Intensity. Is there
> > > quick way to normalize this data set, such that the
> > > area under the curve is 1. Perhaps a very stupid
> > > question, but any leads are much appreciated.
> > > >
> > > > It's not a stupid question.
> > > > What it is is lacking in detail:
> > > > 1. Are the t equispaced?
> > > > 2. You say the area is to be unity, but how does
> > > that work in terms
> > > > of units? e.g., if time is in seconds and
> > > intensity is in N/m^2, then
> > > > the area will be N-s /m^2. How can that be unity?
> > >
> > > Thanks for your response and apologies for being a
> > > bit vague. So basically what I have is a
> > > step-response of my instrument (I vs. t). I
> > > differentiate this to get an impulse response
> > > (dI/dt). Now I want to be able to convolve this
> > > impulse response with an arbitrary input to generate
> > > the output.
> > > If I normalize the impulse response such that the
> > > area under the curve is 1, the the output maintains
> > > the same amplitudes as the input (except that now it
> > > is convolved).
> > > To answer your specific question:
> > > 1. Yes, t is equispaced.
> > > 2. For the units: since its the area for the impulse
> > > response, so that is (dI/dt)*dt = I should be 1.
> > > Basically, as I said before, I don't know how to
> > > quickly implement a code so as to normalise a
> > > data-set of x,y values.
> > > Thanks again!
> >
> > ynorm=y./trapz(x,y) ?
> >
> > Best wishes
> > Torsten.
>
>
> Works! Thanks very much !


Btw, how would this work is x was not evenly spaced? if I am correct, trapz (x,y) only works well when x is evenly spaced.

"Desert Hike" <deserthike@gmail.com> wrote in message
news:ij4ac7$d$1@fred.mathworks.com...

*snip*

> Btw, how would this work is x was not evenly spaced? if I am correct,
> trapz (x,y) only works well when x is evenly spaced.

Why do you think that?

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Steve Lord
slord@mathworks.com
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