fourier.transform {freqdom}

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)

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.

Value

An object of class freqdom.

See Also

fourier.inverse

Examples

# 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)