freqdom.transpose: Compute a transpose of a given frequency-domain operator at...

In freqdom: Frequency Domain Based Analysis: Dynamic PCA

Compute a transpose of a given frequency-domain operator at each frequency

Description

For a given frequency-domain operator S (freqdom) the function freqdom.transpose computes the transpose of S_θ' at each frequency from the evaluation grid.

Usage

freqdom.transpose(x)

Arguments

S	a frequency-domain filter of type freqdom, i.e. a set of linear operators S_k \in \mathbf{R}^{p_1 \times p_2} on some discreet grid defined of [-π,π].

Details

Let S = \{ S_θ : θ \in G \}, where G is some finite grid of frequencies in [-π,π] and S_θ \in \mathbf{C}^{p \times p}. At each frequency θ \in G function freqdom.transpose transposes

Resulting object is defined as

S' = \{ S_θ': θ \in G \}.

Value

Function returns a frequency domain object (freqdom) of dimensions L \times p_2 \times p_1, where L is the size of the grid. The elements of the object correspond to S_θ' as defined above.

freqdom documentation built on Oct. 4, 2022, 5:05 p.m.