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MathGroup Archive 2004

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Re: Reassembling Fourier Transforms

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48868] Re: Reassembling Fourier Transforms
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Sun, 20 Jun 2004 02:39:20 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 6/19/04 at 4:31 AM, lfis at helix.nih.gov (Lee Fisher) wrote:

>I am trying to turn a list of points into a function, and one of
>the ways I thought to do this was to use Fourier to find the
>frequency components of the list, and then to Create a sum of
>exponentials as follows:

<code snipped>

>I have two questions concerning this.  First, is there an easier
>way to turn a set of random values into a function so that NDSolve
>can move through the function and always find the same value at a
>given point (i.e. c[6] will always equal .6002)? 

Yes, there is an easier way. Use Interpolation. For example

In[1]:=
data=Table[Random[],{15}];
f=Interpolation[data]

Out[2]=
InterpolatingFunction[]

In[3]:=
f[5]

Out[3]=
0.615588
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