Reconstruction of Time-Series Records from Their Modes

Adds up, for each series of the tables of decomposeTSL, the modes that a selection retains and, unless excluded, the remainder of the series.

Usage

reconstructTSL(decomposition, selection, includeResidue = TRUE)

Arguments

decomposition: The list of tables of decomposeTSL, as for measureModesTSL. It is not modified.
selection: A table with the keys and mode of every mode of decomposition, once each, and retained, TRUE or FALSE, as the table selection of selectModesTSL. It is not modified.
includeResidue: TRUE, the default, adds the remainder of each series, residue or fitResidual; FALSE leaves it out.

Details

The reconstruction of a series is the sum of its retained modes and, with includeResidue, its remainder. A series without retained modes sums zero, and a method without remainder, as decomposeEWT, adds none. With every mode and the remainder, the result follows the reconstruction relation of the selected method. For EMD the sum recovers the input up to rounding. In decomposeEEMD with the divisor "realizations", it gives the signal plus meanNoise. The order of the rows of the tables does not intervene.

A partial sum implements the declared selection; neither the sum nor the choice to include a remainder establishes that the result is free of noise.

Value

A named list with one data.table table, reconstruction: the keys of decomposition, t and s, on the grid and in the order of signal.

Examples

Time <- seq(0, 9, length.out = 3000)
Signal <- sin(pi * Time) + sin(2 * pi * Time) + sin(6 * pi * Time) +
    0.5 * Time
# The same series under three IDs and three components.
TSL <- data.table::rbindlist(lapply(c("AT", "VT", "DT"), function(id) {
    data.table::rbindlist(lapply(c("H1", "H2", "UP"), function(ocid) {
        data.table::data.table(ID = id, OCID = ocid, t = Time, s = Signal)
    }))
}))
Sifting <- list(stopRule = "doubleThreshold")
Decomposition <- decomposeTSL(TSL, method = "decomposeEMD",
                              control = list(sifting = Sifting),
                              by = character())
Metrics <- measureModesTSL(Decomposition)$metrics
# A minimum energy fraction of zero retains every mode: with the residue,
# the reconstruction is the signal.
Every <- selectModesTSL(Decomposition, metrics = Metrics,
                        criterion = list(rule = "energyFraction", minimum = 0,
                                         action = "keep"))
Complete <- reconstructTSL(Decomposition, selection = Every$selection)
max(abs(Complete$reconstruction$s - Decomposition$signal$s))
#> [1] 1.332268e-15
# The modes in [2, 15] Hz, without the residue.
Band <- selectModesTSL(Decomposition, metrics = Metrics,
                       criterion = list(rule = "band", fMin = 2, fMax = 15,
                                        action = "keep"))
Filtered <- reconstructTSL(Decomposition, selection = Band$selection,
                           includeResidue = FALSE)
head(Filtered$reconstruction)
#>      OCID     ID           t          s
#>    <char> <char>       <num>      <num>
#> 1:     H1     AT 0.000000000 -0.8149686
#> 2:     H1     AT 0.003001000 -0.7334793
#> 3:     H1     AT 0.006002001 -0.6524386
#> 4:     H1     AT 0.009003001 -0.5720312
#> 5:     H1     AT 0.012004001 -0.4924402
#> 6:     H1     AT 0.015005002 -0.4138474