Module memd 

Multivariate Empirical Mode Decomposition (MEMD).

Univariate emd applied independently to each channel of a multivariate signal does not produce mode-aligned IMFs: IMF₂ of channel A may correspond in scale to IMF₃ of channel B, because each channel’s sifting picks its own extrema sequence.

MEMD (Rehman & Mandic, Proc. R. Soc. A, 2010) enforces a common scale alignment by projecting the multivariate residue onto a set of direction vectors in n-dimensional space and computing per-channel envelopes from the projection extrema. Averaging the resulting per-channel mean envelopes across directions yields a multivariate local mean that drives a joint sift, so IMF index k corresponds to the same intrinsic scale on every channel.

Use this transform when channels are correlated (multi-asset baskets, multi-axis sensors, EEG arrays) and you want IMF-based features that are comparable across channels. For independent channels, the cost is unjustified — use emd per channel.

Determinism

With DirectionStrategy::Hammersley the result is fully deterministic (no RNG). With DirectionStrategy::Uniform and a fixed MEMDConfig::random_seed the result is bitwise-identical across runs: direction vectors are pre-generated sequentially from a single seeded StdRng, then their per-direction envelope contributions are computed in parallel via [rayon] but reduced in fixed direction-index order. The summation pattern matches the prior sequential implementation, so IMFs are bitwise-identical across runs and across RAYON_NUM_THREADS values.

References

• Rehman, N., & Mandic, D. P. (2010). Multivariate empirical mode decomposition. Proc. R. Soc. A, 466(2117), 1291–1302. https://doi.org/10.1098/rspa.2009.0502
• Rehman, N., & Mandic, D. P. (2011). Filter bank property of multivariate empirical mode decomposition. IEEE Trans. Signal Processing, 59(5), 2421–2426. https://doi.org/10.1109/TSP.2011.2106779
• Rilling, G., Flandrin, P., & Gonçalves, P. (2003). On empirical mode decomposition and its algorithms. IEEE-EURASIP Workshop NSIP-03.
• Fang, K.-T., & Wang, Y. (1994). Number-Theoretic Methods in Statistics. Chapman & Hall — Hammersley/Halton point construction basis.
• Reference MATLAB implementation (Mandic group): http://www.commsp.ee.ic.ac.uk/~mandic/research/emd.htm

Structs

MEMDConfig

Configuration for memd.

MEMDResult

MEMD decomposition result.

Enums

DirectionStrategy

How to generate the n-dimensional direction vectors used by MEMD.

Functions

hammersley_sphere

Hammersley point sequence mapped to the unit (n − 1)-sphere via inverse-normal-CDF + normalize (Marsaglia method on a low-discrepancy sequence). Returns k row vectors of length n, each unit-norm and asymptotically uniform on the sphere for any n as k → ∞.

memd

Perform Multivariate Empirical Mode Decomposition.