| 93 | | The spectra object uses a parallelized version of the FFT function. The 1D FFT calculates |
| | 93 | The 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 | |
| | 97 | where [[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 | |
| | 101 | so while we can calculate the transform for any k, only N of them will be unique. |
