Reconstruct Wavelet Components from Selected Scales (CWT)

Reconstructs time-domain components from selected wavelet scales using the Torrence & Compo (1998) inverse transform approximation. Optionally adds a residual component representing non-selected scales to ensure additive closure.

Note: CWT-reconstructed components are additive but NOT orthogonal due to scale overlap. For MODWT additive decomposition, use analyze_wavelet_additive.

Usage

extract_wavelet_components(
  wave,
  signif_periods,
  scale,
  dj = 0.25,
  dt = 1,
  series_sd,
  series_mean = 0,
  Cdelta = 0.776,
  w0_0 = pi^(-1/4),
  include_residual = TRUE
)

Arguments

wave

Complex matrix (scales x time). Wavelet coefficients.

signif_periods

Integer vector. Scale indices to reconstruct.

scale

Numeric vector. Scale values aligned with nrow(wave).

dj

Numeric scalar. Scale resolution used in the transform.

dt

Numeric scalar. Time step of the series.

series_sd

Numeric scalar. Standard deviation of the original series (pre-standardization).

series_mean

Numeric scalar. Mean of the original series; added back to residual.

Cdelta

Numeric scalar. Morlet reconstruction constant (default: 0.776).

w0_0

Numeric scalar. psi_0(0) constant (default: pi^(-1/4)).

include_residual

Logical. If TRUE, adds a residual (non-selected) component.

Value

Numeric matrix with one column per selected component and, if requested, a final "Noise" residual column.

References

Torrence, C., & Compo, G. P. (1998). A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79(1), 61-78.

See also

analyze_wavelet_spectrum, analyze_wavelet_additive