pyFDN.filter_matrix_gallery

pyFDN.filter_matrix_gallery(N=None, matrix_type=None, *, num_stages=3, sparsity=3.0, stage_matrix_type='Hadamard')

Return an FIR (filter) feedback matrix of the requested type, or list all type names.

Overloads:

• N (int), matrix_type (str), num_stages (int), sparsity (float), stage_matrix_type (str) → np.ndarray

• N (int | None), matrix_type (None), num_stages (int), sparsity (float), stage_matrix_type (str) → list[str]

• N (None), matrix_type (str), num_stages (int), sparsity (float), stage_matrix_type (str) → NoReturn

All types are paraunitary (lossless): A^T(z^{-1}) A(z) = I. Used as scattering feedback matrices in an FDN (Schlecht & Habets 2020).

Parameters:

• N (int | None) – Matrix size. Ignored when matrix_type is None.

• matrix_type (str | None) – One of "random_dense" (dense cascaded paraunitary matrix), "velvet" (sparse velvet-noise feedback matrix), or "from_elementals" (cascade of degree-one lossless factors, polynomial degree N * num_stages); the historical fdnToolbox spellings ("Velvet", …) are accepted. Pass None (or call with no arguments) to get the list of all type names.

• num_stages (int) – Number of cascade stages (or degree factor for "from_elementals").

• sparsity (float) – Sparsity of the "velvet" type (ignored otherwise).

• stage_matrix_type (str) – Stage matrix for "random_dense" and "velvet": "Hadamard" or "random" (random orthogonal; avoids the structural double poles at z = ±1 of Hadamard stages).

Returns:

Feedback matrix of shape (N, N, L) in z^{-1} convention, or a list of type-name strings.

Example:

filter_matrix_gallery()              # → list of type strings
filter_matrix_gallery(4, "velvet", num_stages=3, sparsity=3)