Why Img2Num Uses the DFT

1. Inputs are digital — images and arrays are sampled and finite; the DFT exactly models the transform we can compute on them.
2. Finite memory — continuous transforms need infinite support; DFT works with finite-length vectors held in RAM.
3. Efficient algorithms exist — the FFT computes the DFT quickly ($O(N\log N)$ rather than $O(N^2)$).
4. Discrete manipulations match implementation — convolution via multiplication in frequency domain, frequency-domain filters (Gaussian, high/low-pass) operate on bins.
5. Compatibility with image processing conventions — 2D DFT is separable: apply 1D DFT across rows then columns (or vice versa); per-channel processing is straightforward.

Practical consequences to document in the repo

• Zero-padding to reduce circular convolution effects.
• Windowing to reduce spectral leakage.
• fft shift / ifft shift to center the zero frequency for visualization.
• Explain per-channel transforms for multi-channel images (RGB).