THEORY OF DIGITAL FILTER BANKS REALIZED VIA MULTIVARIATE EMPIRICAL MODE DECOMPOSITION

Undecimated and decimated multivariate empirical mode decomposition filter banks (MEMDFBs) are introduced in order to incorporate MEMD equipped with downsampling into any arbitrary tree structure and provide flexibility in the choice of frequency bands. Undecimated MEMDFBs show the same results as those of original MEMD for an octave tree structure. Since the exact cut-off frequencies of MEMD are not known (i.e. due to data-driven decomposition), employing just simple downsampling in MEMD might cause aliasing. However, decimated MEMDFBs in this paper achieve perfect reconstruction with aliasing cancelled for any arbitrary tree. Applications of decimated/undecimated MEMDFBs for speech/audio and image signals are also included. Since decimated MEMDFBs can be applied into any arbitrary tree structure, this extends into MEMD packets. Arbitrary tree structures in decimated MEMDFBs also lead to more diverse choices in frequency bands for various multivariate applications requiring decimations.