Empirical Mode Decomposition

Formula: iterative sifting into intrinsic mode functions. Given the running residual r, the sifting loop of Huang et al (1998) sec. 4 is

1. locate the local maxima and minima of h;

2. cubic-spline the maxima into an upper envelope u and the minima into a lower envelope l;

3. m = (u + l) / 2 ; h <- h - m;

4. stop when SD = sum (h_k - h_{k-1})^2 / sum h_{k-1}^2 < sd_tol (Huang eq. 5.5, recommended 0.2-0.3).

The extracted h is an IMF; it is subtracted from r and the loop repeats until the residual has fewer than three extrema or max_imf IMFs have been taken. Endpoints are appended to both extremum sets so the envelopes span the record.

Usage

Emdtsm(y, max_imf = 10, max_sift = 50, sd_tol = 0.2)

Arguments

y

Signal.

max_imf

Maximum number of IMFs to extract.

max_sift

Maximum sifting iterations per IMF.

sd_tol

Cauchy-type stopping threshold SD.

Value

List with estimate, n_imf, imfs (row-major), residual, completeness, n, method.

References

Huang, Shen, Long, Wu, Shih, Zheng, Yen, Tung & Liu (1998), Proc. R. Soc. Lond. A 454(1971):903-995, doi:10.1098/rspa.1998.0193.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Emdtsm(V)
#> $estimate
#> [1] 0
#> 
#> $n_imf
#> [1] 0
#> 
#> $imfs
#> numeric(0)
#> 
#> $residual
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $completeness
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Empirical Mode Decomposition"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"