freqdom.product {freqdom}R Documentation

Compute a matrix product of two frequency-domain operators

Description

For given frequency-domain operators F and G (freqdom) the function freqdom.kronecker computes their matrix product frequency-wise.

Usage

freqdom.product(F, G)

Arguments

F

frequency-domain filter of type freqdom, i.e. a set of linear operators F_\theta \in \mathbf{R}^{p \times q} defined on a discreet grid defined S \subset [-\pi,\pi].

G

frequency-domain filter of type freqdom, i.e. a set of linear operators G_\theta \in \mathbf{R}^{q \times r} defined on a discreet grid defined S \subset [-\pi,\pi].

Details

Let F = \{ F_\theta : \theta \in S \}, G = \{ G_\theta : \theta \in S \}, where S is a finite grid of frequencies in [-\pi,\pi], F_\theta \in \mathbf{C}^{p \times q} and G_\theta \in \mathbf{C}^{q \times r}.

We define

H_\theta = F_\theta G_\theta

as a matrix product of F_\theta and G_\theta, i.e. H_\theta \in \mathbf{R}^{p\times r}. Function freqdom.product returns H = \{ H_\theta : \theta \in S \}.

Value

Function returns a frequency domain object (freqdom) of dimensions L \times p \times r, where L is the size of the evaluation grid. The elements correspond to F_\theta * G_\theta defined above.

Functions

Examples

n = 100
X = rar(n)
Y = rar(n)
SX = spectral.density(X)
SY = spectral.density(Y)
R = freqdom.product(SY,SX)

[Package freqdom version 2.0.3 Index]