Inelastica.math.hilbert.Hilbert(f, ker=None)[source]

Hilbert transform \(\mathcal{H}[f](y)\) of a function \(f(x)\) with finite support, sampled on an equidistant grid \(\{x_1,x_2,x_{nh}\}\).

Definition:

\(\mathcal{H}[f](y)= \frac{1}{\pi} p.v.\int_{-\infty}^{\infty} dx \frac{f(x)}{x-y}\).

Parameters:
fndarray

List of function values \(f(x)\).

kerndarray (optional)
Returns:
Hfndarray

Hilbert transform of \(f(x)\).

kerndarray

Kernel function, can be reused for other transformations with the same number of grid points.