Re: Reassembling Fourier Transforms

• To: mathgroup at smc.vnet.net
• Subject: [mg48929] Re: Reassembling Fourier Transforms
• From: astanoff_otez_ceci at yahoo.fr (astanoff)
• Date: Thu, 24 Jun 2004 05:35:46 -0400 (EDT)
• References: <cb0ut2\$r67\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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
[...]
Why not simply use Interpolation?
(InterpolatingFunction is compatable with NDSolve)
For instance :

In[1]:=<<Statistics`ContinuousDistributions`

In[2]:=f[x_]:=Random[NormalDistribution[0,1]]

In[3]:=tf=Table[{x,f[x]},{x,1,20}];

In[4]:=c=Interpolation[tf, InterpolationOrder -> 1];

In[5]:=
sol=First@NDSolve[y'[u] == y[u]/10+c[u] && y[1] == 1,y[u],{u,1,20}]

Out[5]={y[u] -> InterpolatingFunction[{{1.,20.}},<>][u]}

In[6]:=g[u_]=y[u] /. sol

Out[6]=InterpolatingFunction[{{1.,20.}},<>][u]

hth
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```

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