Convolution Integrals
- To: mathgroup at smc.vnet.net
- Subject: [mg16807] Convolution Integrals
- From: "Mortimer, Martin" <M.MORTIMER at CGIAR.ORG>
- Date: Tue, 30 Mar 1999 02:35:12 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Dear all:
I am a new user of Mathematica and very much still on the learning
curve, so
I would be extremely grateful for some help.
The background
-----------------------
I need to do convolution integrals of various combinations of Gaussian
(Normal) and Lognormal functions, sometimes in pairs, sometimes in
threesomes and maybe more. It seems to me that the easiest way to do
this is
through the inverse fourier transform of the product of the fourier
transforms of the functions.
The problem
-----------------
Here is a simple example of the code in the approach I have used so
far.
In[1]:= <<Statistics`ContinuousDistributions`
In[2}:= <<Calculus`FourierTransform`
In[3]:= dist1=NormalDistribution[10,3]
Out[3]= NormalDistribution[10, 3]
In[4]:= pdf1=PDF[dist1,x]
Out[4]=
1
---------------------------
2
(-10 + x) /18
3 E Sqrt[2 Pi]
In[5]:= Plot[%,{x,0,20}]
-Graphics-
In[6]:= dist2=NormalDistribution[5,4]
Out[6] = NormalDistribution[5, 4]
In[7]:= pdf2=PDF[dist2,x]
Out[7] =
1
--------------------------
2
(-5 + x) /32
4 E Sqrt[2 Pi]
In[8]:= trans1=FourierTransform[pdf1,x,s]
Out[8] =
2
10 I s - (9 s )/2
E
In[9]:= trans2=FourierTransform[pdf2,x,s]
Out[9] =
2
5 I s - 8 s
E
In[10]:= conv=InverseFourierTransform[trans1 trans2]
Out[10] =
2
15 I s - (25 s )/2
InverseFourierTransform[E ]
Question :
I seem to be able to get to the inverse transform alright but how do I
plot
the final distribution ?
I would be very grateful for some clear code on how to do this that I
can
comprehend.
I have looked in the archives and whilst there has been some discussion
on
this topic, I still cannot workout a way forward.
For the curious, my work is concerned with the prediction of weed
occurrence
in rice fields and we are trying to develop a model that can predict
the
likelyhood of weed germination, establishment and ultimately yield
loss.
Thanking you in advance
Martin Mortimer
_____________________________________________________________________
Dr Martin Mortimer
Weed
Ecologist
International Rice Research Institute,
P. O. Box 3127
Makati Central Post Office(MCPO)
1271 Makati City
Philippines
Telephone: (63) 2 845 0563 / 0569
ext : - office 771 / 221 ; - home 249
E-mail: M.MORTIMER at CGIAR.ORG
Fax: (63) 2 891 1292 or (63) 2 845 0606
Personal E-mail in UK: Greywing at compuserve.com
"IRRI is one of 16 centers supported by the Consultative Group on
International Agricultural Research (CGIAR). http://www.cgiar.org/irri
<http://www.cgiar.org/irri> ."
_____________________________________________________________________