fourier.transform: Computes the Fourier transformation of a filter given as timedom object
Description
Computes the frequency response function of a linear filter and returns it as a freqdom object.
Usage
fourier.transform(A, freq = pi * -100:100/100)
Value
An object of class freqdom.
Arguments
A
an object of class timedom.
freq
a vector of frequencies \(\in [-\pi, \pi]\).
Details
Consider a filter (a sequence of vectors or matrices) \((A_k)_{k\in A\$lags}\). Then this function computes
$$\sum_{k\in A\$lags} A_k e^{-ik\omega}$$
for all frequencies \(\omega\) listed in the vector freq.
# We compute the discrete Fourier transform (DFT) of a time series X_1,..., X_T.X = rar(100)
T=dim(X)[1]
tdX = timedom(X/sqrt(T),lags=1:T)
DFT = fourier.transform(tdX, freq= pi*-1000:1000/1000)