Changes between Version 13 and Version 14 of SpectraObject


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Timestamp:
01/12/15 13:18:22 (10 years ago)
Author:
Jonathan
Comment:

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  • SpectraObject

    v13 v14  
    9191
    9292== What does the Spectra calculate? ==
    93 The spectra object uses a parallelized version of the FFT function.  The 1D FFT calculates
     93The Spectra performs a DFT on whatever fields  are assigned to it.  The discrete FFT is defined as
     94
     95[[latex($F_k=\displaystyle \sum_{x=1}^{N_x} e^{  \frac{2 \pi i}{N_x} k x} f_{x}$)]]
     96
     97where [[latex($k$)]] is any integer.  Now [[latex($F_k$)]] is periodic in [[latex($k$)]] since
     98
     99[[latex($F_{k+N_x}=\displaystyle \sum_{x=1}^{N_x} e^{  \frac{2 \pi i}{N_x} \left(k+N_x\right) x} f_{x} = \displaystyle \sum_{x=1}^{N_x} e^{2 \pi i x} \times e^{  \frac{2 \pi i}{N_x} k x} f_{x}=\displaystyle \sum_{x=1}^{N_x} e^{  \frac{2 \pi i}{N_x} kx} f_{x}  =F_k$)]]
     100
     101so while we can calculate the transform for any k, only N of them will be unique.
    94102
    95103[[latex($F_l=\displaystyle \sum_{l'=1}^{N_x} e^{  \frac{2 \pi i}{N_x} (l-1) (l'-1)} f_{l'}$)]]