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

 fourier.transform R Documentation

## 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 [-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

# 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)


freqdom documentation built on April 18, 2022, 5:05 p.m.