       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

>

>

```

• Prev by Date: Re: Definite Integration in Mathematica
• Next by Date: Re: Thread function now working as expected
• Previous by thread: Symbolic Calculations with Matrices
• Next by thread: Self-Teaching Snag - Thank you!