Undecimated and Decimated EMD Non-Uniform Filterbanks Approximating Critical Bands

Abstract

This paper presents a novel set of critical band filterbanks, i.e. filters that mimic the human auditory system (HAS). The filterbanks are based on the empirical mode decomposition (EMD). Two cases are investigated: decimated and undecimated filters. Since the HAS does not follow conventional linear and stationary properties, non-uniform filterbanks approximating critical bands with EMD are developed. The EMD is a data-driven decomposition and, as such, is well suited to deal with nonlinear and nonstationary signals. Thus, it is natural that it is good fit for modeling the HAS both for speech and audio systems. As an application of the developed non-uniform filterbanks, noise removal is applied into each EMD critical band so that the auditory masking effect within the critical bands can be utilized in speech enhancement with the properties of EMD. The speech enhancement in the proposed EMD critical bands is compared in this paper with a speech enhancement algorithm that removes colored noises through simultaneous diagonalization of covariance matrices. Since the proposed filterbanks are very flexible in designing arbitrary tree structures, it is expected they can be used in various applications.

Theory of Digital Filter Banks Realized via Multivariate Empirical Mode Decomposition

“…However, the theory of filter banks based on MEMD is still lacking. Hence, similar idea to Koh and Rodriguez-Marek [2013a, 2013b, 2013c] is adopted in this paper to design MEMD filter banks (MEMDFBs), resulting in an adaptive data-derived T-F plane. Moreover, since MEMDFBs is applicable into any arbitrary tree structure, it will be extended in this paper into MEMD and/or NA-MEMD packets coined by similar name to wavelet packets.…”

“…In this paper, undecimated MEMDFBs are designed by extending the concept of undecimated EMDFBs in Koh and Rodriguez-Marek [2013b]. To make a filter bank structure with MEMD, just one IMF and one residual are considered at each decomposition step, like EMDFBs in Rodriguez-Marek [2013a, 2013b].…”

“…1, the node signals, X 10 and X 11 , are corresponding respectively to one residual and one IMF of the mother node signal, X 00 . Figure 1 is similar to those in Koh and Rodriguez-Marek [2013b] except for the use of MEMD in order to accommodate multivariate signals. Since MEMD in Mandic et al [2013] and Rehman and Mandic [2010] shows a good mode-splitting property at each IMF, an octave tree structure in undecimated MEMDFBs shows the same results as those of MEMD.…”

“…To overcome those drawbacks of original EMD, EMDFBs are introduced in Koh and Rodriguez-Marek [2013a, 2013b, 2013c as an extension of Huang et al [1998] into filter bank theory. EMDFBs introduced in Koh and Rodriguez-Marek [2013a, 2013b, 2013c] incorporate downsamplings to reduce decomposed data and it is applicable into any arbitrary tree structure so that chosen frequency bands are flexible to create any nonuniform filter banks. Figure 3 shows one stage of analysis and synthesis filter banks in decimated EMDFBs.…”

“…Since there are no traditional filters involved in EMD, any simple down/up sampling process ends up with failure of perfect reconstruction. To resolve the problem, downsampling with even and odd indices is introduced for 1D/2D signals and named as EMD filter banks (EMDFBs) in Koh and Rodriguez-Marek [2013a, 2013b, 2013c. The EMDFBs provide perfect reconstruction without any traditional filters, while keeping all desirable characteristics of EMD.…”