# fourier.transform: Computes the Fourier transformation of a filter given as... In freqdom: Frequency Domain Based Analysis: Dynamic PCA

## Description

Computes the frequency response function of a linear filter and returns it as a freqdom object.

## Usage

 1 fourier.transform(A, freq = pi * -100:100/100) 

## Arguments

 A an object of class timedom. freq a vector of frequencies \in [-π, π].

## Details

Consider a filter (a sequence of vectors or matrices) (A_k)_{k\in A\$lags}. Then this function computes ∑_{k\in A\$lags} A_k e^{-ikω}

for all frequencies ω listed in the vector freq.

## Value

An object of class freqdom.

fourier.inverse

## Examples

 1 2 3 4 5 6 # 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) 

### Example output

Loading required package: mvtnorm