Re: Fourier Transforms for Idiots?
- To: mathgroup at smc.vnet.net
- Subject: [mg37626] Re: [mg37588] Fourier Transforms for Idiots?
- From: "Y.A.Tesiram" <yas at pcomm.hfi.unimelb.edu.au>
- Date: Wed, 6 Nov 2002 06:58:52 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hi Ron,
Yes you can virtually plug any values in and something will be returned.
But a little background will help.
Below is an example of two frequencies in phase. Copy the text below into
a notebook and evaluate. You need the MultipleListPlot package for this
example.
Generally Fourier transforms are used to sample multiple frequencies from
one data set and so you end up with a spectrum of frequencies. As in the
ListPlot part below I have plotted the positive part only which clearly
shows that there are two frequencies present. Also have a look at Re and
Im instead of Abs. You will need to change the PlotRange. Try
PlotRange->All.
<< Graphics`MultipleListPlot`
f1 = Table[Sin[x], {x, -5*N[Pi], 5*N[Pi], 0.05*Pi}];
f2 = Table[Sin[0.2*x], {x, -5*N[Pi], 5*N[Pi], 0.05*Pi}];
f3 = f1 + f2;
MultipleListPlot[{f1, f2, f3}, PlotJoined -> True,
SymbolShape -> {None, None, PlotSymbol[Box]}]
ListPlot[Abs[Fourier[f1]],
PlotJoined -> True, PlotRange -> {{0, 20}, {0, 10}}]
ListPlot[Abs[Fourier[f2]], PlotJoined ->
True, PlotRange -> {{0, 20}, {0, 10}}]
ListPlot[Abs[Fourier[f3]], PlotJoined -> True, PlotRange -> {{0, 20}, {0,
10}}
]
Yas
On Tue, 5 Nov 2002, Ron Hubbard wrote:
> For a research project I need to know if radio waves of
> various frequencies are either constructively or destructively
> interfering with each other. I was told Fourier transforms are
> good for this purpose, but I am mathematically challenged and
> have problems with 2+2.
>
> How complicated is it to use Mathematica to determine these
> kinds of interactions? Does anyone know of any software or
> programs available where values can be plugged in without
> having to know a lot of math?
>
> Thanks.
>
>
>
>