Lookup for spectrum with different delta WL

[g1lai]

I am trying to do spectral integration for the spectrum with different wavelength interval. I think lookup function can be used for this application, but something is wrong in my programming ...

[TomGutman]

You need interpolation, not lookup.
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� � � � Tom Gutman

[RichardJ]

See the attached worksheet.

Richard

[TomGutman]

You're pretty brave, doing a cubic spline on such jagged data. Doesn't make much diffference to the integral, though.

But why did you limit the integration to 300-1000 when the data appear to be available from 280 to 1200?
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� � � � Tom Gutman

[TheodoreM.Bones]

There are too many tasks set out on the work. Confining myself to the integration problem, I have run it OK, although it is right slow due to the number of points involved. Good agreement with your cspline function is done.

[RichardJ]

On 7/28/2009 8:03:50 PM, Tom_Gutman wrote:
>You're pretty brave, doing a
>cubic spline on such jagged
>data.

Not really. I looked at it on a fine mesh, and decided it was 6 of one and half a dozen of the other. As an example, picking one strong absorption band, if you were to look at 758.6 at the edge of the band the spline is clearly wrong, and a linear interpolation would be closer. On the other hand, if you look at the absorption maximum at 760.6 the spline is clearly better than the linear interpolation.

> Doesn't make much
>diffference to the integral,
>though.

I didn't bother to check that, but it doesn't surprise me. Neither interpolant is ideal, and I suspect that the high and low errors somewhat cancel in both cases.

It makes things a little painful that the spectral data has unequal x. There are delta x values of 0.5, 1, 2, 3, and 5. If they were equal a good approach would be to FFT the data, zero pad, apodize, and IFFT to increase the data point density. With a suitable choice of apodization you get a good preservation of band shape. I suppose this could still be done, by breaking the data into chunks, but it's too much work 🙂

>But why did you limit the
>integration to 300-1000 when
>the data appear to be
>available from 280 to 1200?

I didn't know what the desired range was, so I just picked some numbers that were within the allowed limits.

Richard

[RichardJ]

On 7/29/2009 8:19:58 AM, jmG wrote:

>I borrowed Theodore 11

Unfortunately, Theodore deleted a large, and very important, chunk of the original worksheet. The objective was not to integrate that data, but rather the product of two pieces of data with non-matching x values and a function. At which point interpolation is required.

Richard

[RichardJ]

On 7/29/2009 11:18:52 PM, jmG wrote:

>I have replied and done the "goal" & the
>"Question"

In neither of the worksheets you posted in this thread did you integrate what was requested.

Richard

[ptc-1368288]

On 7/30/2009 8:31:03 AM, rijackson wrote:
>On 7/29/2009 11:18:52 PM, jmG wrote:
>
>>I have replied and done the "goal" & the
>>"Question"
>
>In neither of the worksheets you posted
>in this thread did you integrate what
>was requested.
>
>Richard
____________________________

The request is to integrate a data set only.
Didn't you introduce the spline, yourself ?
A lost request whereas the collab didn't reply.

jmG

[RichardJ]

On 7/30/2009 11:32:52 AM, jmG wrote:

>The request is to integrate a data set
>only.

No. It was to integrate the product of two data sets and a function.

Richard

[ptc-1368288]

On 7/30/2009 1:59:09 PM, rijackson wrote:
>On 7/30/2009 11:32:52 AM, jmG wrote:
>
>>The request is to integrate a data set only.
>
>No. It was to integrate the product of
>two data sets and a function.
>
>Richard
______________________________

Yes Richard,

I can read same interpretation XX(1499). I did not complete that interpretation intentionally ... our collaboration is $ 0.00 , but a returned work sheet from the visitor costs $$$$. So step one in this project is to understand that the data set AM governs. Nothing else yet. Integrate the AM and for the next step if it makes any sense to have AM multiplied by an unknown other data set, clearly that new one has to be "sized" to the same length than AM ... and if these two must be multiplied by another unknown function , clearly again this function has to be sized and discretized so that the 3 components are compatible. Really a simple task that the originator can figure the next step as suggested XX(1499): linterp + disctretize then dscretize the function. Multiply component wise these 3 vectors of values, plug into the FD integrator = project done.

My point is that I'm not going to apply unknown forgery to the AM data set, especially if it comes from the public domain. Don't get me wrong, I don't refuse doing, just that the forgery has to be sourced c/w an abstract so that this part of an eventual "elastic project" can be tutored and closed.

Jean