freqdom.product {freqdom} | R Documentation |
For given frequency-domain operators F
and G
(freqdom
) the function freqdom.kronecker
computes their matrix product frequency-wise.
freqdom.product(F, G)
F |
frequency-domain filter of type |
G |
frequency-domain filter of type |
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 \}
.
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.
freqdom.product()
: Frequency-wise matrix product of two frequency-domain operators
n = 100
X = rar(n)
Y = rar(n)
SX = spectral.density(X)
SY = spectral.density(Y)
R = freqdom.product(SY,SX)