Theory of Digital Filter Banks Realized via Multivariate Empirical Mode Decomposition

Abstract

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.

Undecimated Non-uniform Multivariate Empirical Mode Decomposition Filter banks for Arbitrary Nodes and its Application for Speech Enhancement Mode Decomposition Filter banks for Arbitrary

“…The MEMD produces IMFs for each one of the channels in the given multivariate signal. To extend the MEMD to MEMDFBs, only the 1 st IMF and one residual are considered [3]. A MATLAB-like pseudo code for the MEMD to be used in MEMDFBs is given in Fig.1.…”

“…The EMD was extended to multivariate EMD (MEMD) in [2] for multichannel applications such as multichannel speech signals, EEG signals etc. Recently, a theory to build non-uniform filter banks using the MEMD was also introduced in [3]. The paper [3] shows how to build decimated/undecimated MEMD filter banks (MEMDFBs) for any arbitrary trees.…”

“…Recently, a theory to build non-uniform filter banks using the MEMD was also introduced in [3]. The paper [3] shows how to build decimated/undecimated MEMD filter banks (MEMDFBs) for any arbitrary trees. However, undecimated MEMDFBs are applicable only to octave trees because many node signals do not exist for other trees, whereas decimated MEMDFBs are available for any arbitrary tree structures [3].…”

“…The paper [3] shows how to build decimated/undecimated MEMD filter banks (MEMDFBs) for any arbitrary trees. However, undecimated MEMDFBs are applicable only to octave trees because many node signals do not exist for other trees, whereas decimated MEMDFBs are available for any arbitrary tree structures [3]. This paper resolves the issue in order to make undecimated MEMDFBs available for arbitrary trees, which are essential for various non-uniform filter banks.…”

Multi-resolution PR NMDFBs for programmable variable bandwidth filter in wideband digital transceivers

“…PR filter banks are very well known in the literature [6][7][8] and recently new techniques for applying PR filter bank trees speech and video processing have been published [11].…”