cbadc.digital_control.utilities.unit_element_set

cbadc.digital_control.utilities.unit_element_set(N: int, M: int, candidates=[-1, 1, 0])

Construct an overcomplete set of vectors only using a single element, i.e.,

\(\mathbf{v} \in \{ - \alpha, \alpha , 0 \}^{N \times M}\)

where duplicates and the \(\begin{pmatrix}0, \dots, 0 \end{pmatrix}\) is excluded from the set.

Parameters

• N (int) – the length of the vectors

• M (int) – the number of unique vectors

• candidates (list[int], optional) – candidates to permute, defaults to [-1, 1, 0].

Returns

a matrix containing the unique vectors as column vectors.

Return type

array_like, shape=(N, M)