fourier.inverse {freqdom} | R Documentation |
Computes Fourier coefficients of some functional represented by an object of class freqdom
.
fourier.inverse(F, lags = 0)
F |
an object of class |
lags |
lags of the Fourier coefficients to be computed. |
Consider a function F \colon [-\pi,\pi]\to\mathbf{C}^{d_1\times d_2}
. Its k
-th Fourier
coefficient is given as
\frac{1}{2\pi}\int_{-\pi}^\pi F(\omega) \exp(ik\omega)d\omega.
We represent the function F
by an object of class freqdom
and approximate the integral via
\frac{1}{|F\$freq|}\sum_{\omega\in {F\$freq}} F(\omega) \exp(i k\omega),
for k\in
lags.
An object of class timedom
. The list has the following components:
operators
\quad
an array. The k
-th matrix in this array corresponds to the k
-th Fourier coefficient.
lags
\quad
the lags of the corresponding Fourier coefficients.
Y = rar(100)
grid = c(pi*(1:2000) / 1000 - pi) #a dense grid on -pi, pi
fourier.inverse(spectral.density(Y, q=2, freq=grid))
# compare this to
cov.structure(Y)