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Re: Symbolic Calculations with Matrices



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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