pyFDN.filter_matrix_gallery#

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

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

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 "RandomDense" (dense cascaded paraunitary matrix), "Velvet" (sparse velvet-noise feedback matrix), or "FromElementals" (cascade of degree-one lossless factors, polynomial degree N * num_stages). 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 "FromElementals").
sparsity (float) – Sparsity of the "Velvet" type (ignored otherwise).
stage_matrix_type (str) – Stage matrix for "RandomDense" and "Velvet": "Hadamard" or "random" (random orthogonal; avoids the structural double poles at z = ±1 of Hadamard stages).

Return type:

ndarray | list[str]

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)