MVAR spectral factorization (transfer function and spectral density)

Turns fitted MVAR coefficients into the frequency-domain quantities used by DTF, PDC and spectral Granger causality. At frequency \(f\), \(\bar{A}(f) = I - \sum_k A_k e^{-2\pi i f k / sr}\), the transfer function is \(H(f) = \bar{A}(f)^{-1}\), and the spectral density is \(S(f) = H(f)\,\Sigma\,H(f)^{*}\).

Usage

.mvarSpectral(A, Sigma, freqs, sr)

Arguments

A

Coefficient array (channels x channels x order).

Sigma

Residual covariance (channels x channels).

freqs

Numeric vector of frequencies in Hz.

sr

Sampling rate in Hz.

Value

A list of complex arrays (channels x channels x length(freqs)): H (transfer function), S (spectral density), A (the \(\bar{A}(f)\) matrices), plus frequencies.

See also

mvarTransfer, .fitMVAR