TFD (topological fluid dynamics) matricial form

banutraul

Homework Statement


Using the matricial form of TFD (discret Fourier Transform) calculated : X=Fd(x) for x=(1,0,2j,1-j)^T from K^4

Homework Equations


X=wx

The Attempt at a Solution


I know the "x" matrix and the "w" matrix but i don't know how to find the "ω" variable from the "w" matrix. "ω" is referring to variable from the TFD direct formula : Σ f(t) [ω][/-mn] ( n=0,N-1)
 
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banutraul said:

Homework Statement


Using the matricial form of TFD calculated : X=Fd(x) for x=(1,0,2j,1-j)^T from K^4

Homework Equations


X=wx

The Attempt at a Solution


I know the "x" matrix and the "w" matrix but i don't know how to find the "ω" variable from the "w" matrix. "ω" is referring to variable from the TFD direct formula : Σ f(t) [ω][/-mn] ( n=0,N-1)
ω^(-mn)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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