# Convert Between mvEWS and Transfer Function Matrices Convert between multivariate evolutionary wavelet spectrum and the set of transfer function matrices. methods ```r 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 ```r ## 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) ```

Spectrum2Transfer function