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freqdom (version 2.0.2)

freqdom.transpose: 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 \(S_\theta'\) at each frequency from the evaluation grid.

Usage

freqdom.transpose(x)

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 \(S_\theta'\) as defined above.

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 \([-\pi,\pi]\).

Details

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

Resulting object is defined as $$S' = \{ S_\theta': \theta \in G \}.$$