Spectrum2Transfer function

Convert Between mvEWS and Transfer Function Matrices

Convert between multivariate evolutionary wavelet spectrum and the set of transfer function matrices. methods

Spectrum2Transfer(object, S2V = TRUE)

Arguments

• object: A mvLSW object containing either the mvEWS or matrix transfer function.

• S2V: Logical, if TRUE (default) then object

  is the mvEWS and the set of transfer function matrices are to be derived. If FALSE the object is the set of transfer function matrices and the converse transformation is derived.

Details

If the mvEWS is supplied, then the set of transfer function matrices are derived by the Choleski factorization of a real symmetric semi-positive definite square matrix. In the cases where the matrix is semi-definite, then the Choleski factorization is applied to the submatrix that is positive definite and the remaining lower triangular elements are populated such that the resulting matrix is a valid factorization.

Conversely, if the set of transfer function matrices are supplied, then the EWS are derived by squaring the matrices.

Returns

A mvLSW object containing either the mvEWS or set of transfer function matrices depending on the specified transformation direction.

References

Taylor, S.A.C., Park, T.A. and Eckley, I. (2019) Multivariate locally stationary wavelet analysis with the mvLSW R package. Journal of statistical software 90 (11) pp. 1--16, doi: 10.18637/jss.v090.i11.

Park, T., Eckley, I. and Ombao, H.C. (2014) Estimating time-evolving partial coherence between signals via multivariate locally stationary wavelet processes. Signal Processing, IEEE Transactions on 62 (20) pp. 5240-5250.

See Also

chol, as.mvLSW, mvEWS.

Examples

## Define evolutionary wavelet spectrum, structure only on level 2
Spec <- array(0, dim=c(3, 3, 8, 256)) ## Ensure all are positive def.
Spec[1, 1, 2, ] <- 10
Spec[2, 2, 2, ] <- c(rep(5, 64), rep(0.6, 64), rep(5, 128))
Spec[3, 3, 2, ] <- c(rep(2, 128), rep(8, 128))
Spec[2, 1, 2, ] <- Spec[1, 2, 2, ] <- punif(1:256, 65, 192)
Spec[3, 1, 2, ] <- Spec[1, 3, 2, ] <- c(rep(-1, 128), rep(5, 128))
Spec[3, 2, 2, ] <- Spec[2, 3, 2, ] <- -0.5

## Define EWS as mvLSW object
EWS <- as.mvLSW(x = Spec, filter.number = 1, family = "DaubExPhase",
  min.eig.val = NA)
plot(EWS, style = 2, info = 2)

## EWS to Transfer function matrices
Transfer <- Spectrum2Transfer(object = EWS, S2V = TRUE)

## Transfer function matrices to EWS
EWS2 <- Spectrum2Transfer(object = Transfer, S2V = FALSE)
plot(EWS2, style = 2, info = 2)