# Chebyshev convolution

## DFT matrix
The following summarizes how the 8-point DFT works, row by row, in terms of fractional frequency:

0 measures how much DC is in the signal
−1/8 measures how much of the signal has a fractional frequency of +1/8
−1/4 measures how much of the signal has a fractional frequency of +1/4
−3/8 measures how much of the signal has a fractional frequency of +3/8
−1/2 measures how much of the signal has a fractional frequency of +1/2
−5/8 measures how much of the signal has a fractional frequency of +5/8
−3/4 measures how much of the signal has a fractional frequency of +3/4
−7/8 measures how much of the signal has a fractional frequency of +7/8
## Chebyshev basis

## Eigen vectors

## Fourier coefficient
$a_{v}=\frac{1}{T}\int_{t_{0}}^{t_{0} + T}f(t)dt$

## Chebyshev coefficient
$g_θ(Λ) = diag(θ)$, (2)
where the parameter $θ ∈ R^n$ is a vector of Fourier coefficients


A single Chebyshev filter (K=3 on the left and K=20 on the right) trained on MNIST and applied at different locations (shown as a red pixel) on a irregular grid with 400 points. Compared to filters of standard ConvNets, GNN filters have different shapes depending on the node at which they are applied, because each node has a different neighborhood structure.

[Wavelets on Graphs via Spectral Graph Theory](https://arxiv.org/pdf/0912.3848.pdf)
{%pdf https://arxiv.org/pdf/0912.3848.pdf %}