# peak deconvolution

Started by January 30, 2004
```hello,

i am working on project of x-ray diffractometer.
Basically the type of distribution for x-ray pattern is poisson type.

i want to know the names of the algorithms which can be used for peak
deconvolution on x-ray diffraction patterns and the link of the site
or documents which describes the algorithms? which algorithm should we
use for x-ray diffraction profile?

Is peak fitting is same as peak deconvolution? what is the diffrence
betn these two?

bye,
amit
```
```Hello Amit,

Basically the measured data from your experiment can be described as the sum
of two random variables. The 1st is the signal and the 2nd is the noise.
When two random variables are added, the resulting distribution is the
convolution of their individual distributions. So in layman's terms, the
noise tends to spread out your signal. I assume the problem is you want to
locate regions of peak energy and the additive noise has blurred the signal.
Peak fitting refers to trying to fit the expectation function to your data.
Imagine your graphed your data out and then you slide the expectation
function left and right until it fits best. But since your data is blurred
by the noise, the fit has a fair bit of uncertainty. Now if you know the
noise function hence its distribution, then you deconvolve your signal plus
noise when the noise function. This will sharpen (make the peaks more
apparent by narrowing them). So a peak fit is now easier. Deconvolution can
be done in several ways. On common way would be to find the DFTs of both
your signal plus noise and the noise functions and divide the noise DFT into
the signal plus noise DFT and finally inverse DFT the quotient. You will
have to be careful about dividing by zero, so you can limit the process by
having a small additive constant in the DFT of the noise function. Things to
look up are deblurring and deconvolution.

--
Clay S. Turner, V.P.
Wireless Systems Engineering, Inc.
Satellite Beach, Florida 32937
(321) 777-7889
www.wse.biz
csturner@wse.biz

"amit" <dreamamit2001@yahoo.com> wrote in message
> hello,
>
> i am working on project of x-ray diffractometer.
> Basically the type of distribution for x-ray pattern is poisson type.
>
> i want to know the names of the algorithms which can be used for peak
> deconvolution on x-ray diffraction patterns and the link of the site
> or documents which describes the algorithms? which algorithm should we
> use for x-ray diffraction profile?
>
>
> Is peak fitting is same as peak deconvolution? what is the diffrence
> betn these two?
>
>
>
> bye,
> amit

```
```amit wrote:

> i am working on project of x-ray diffractometer.
> Basically the type of distribution for x-ray pattern is poisson type.

(snip)

> Is peak fitting is same as peak deconvolution? what is the diffrence
> betn these two?

One of my favorite signal processing books, though not
exactly a DSP book, is something like: "Deconvolution, with
applications to spectroscopy." by Jansson.

If you don't have that one, I would definitely get one.  You might
find it in a good physics or engineering library.

There is a second edition with much more than the first edition.

I don't remember if there are specific examples of x-ray
diffraction, though most examples are optical.  I think the
problems and algorithms should be applicable, though.

-- glen

```