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Re: Symbolic Calculations with Matrices
*To*: mathgroup at smc.vnet.net
*Subject*: [mg74602] Re: Symbolic Calculations with Matrices
*From*: dh <dh at metrohm.ch>
*Date*: Wed, 28 Mar 2007 01:38:14 -0500 (EST)
*References*: <euam5d$d91$1@smc.vnet.net>
Hi Sameer,
your question is not very clear, but it all smells very much like
discrete FFT. Therefore, I assume you want to calculate the FFT of a
given finite time series f[[i]]. Well this is, besides normalization issues:
Sum[f[[i]] Exp[-2 Pi I j i /n],{i,0,n-1}]
This can efficiently be calculated by a dot product of f with:
kernel[j_]:=Table[Exp[- 2 Pi I i j/n],{i,0,n-1}]
The FFT at j can then be obtained by: kernel[j].f
Or we can calculate the whole transformation matrix at once by:
fftmat=Table[kernel[j],{j,0,n-1}]
and obtain the fft of f by: fftmat.f
Daniel
sameer wrote:
> Dear All,
>
> Greetings...I am new to Mathematica and hence my question would be
> trivial to most of you. I tried to find an answer to this from the
> previuos posts but unfortunately I could n't locate any answer.
>
> I have to do various matrix operation like derivatives, inverse etc,
> where each element of the matrix is a matrix/vector. {eg. 1,
> exp(j2*pi*/N), exp(j3*pi*/N)...., exp(j((N-1)*pi*/N} or it could be an
> FFT matrix.
>
> My question is how can I specify such vectors or matrices with the
> range of values as symbolic expressions in the range, 0 to N-1.
>
> Any help is greatly appreciated..
>
> With Thanks and Best Regards
>
> Sameer
>
>
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