Perfect reconstructable decimated two-dimensional empirical mode decomposition filter banks

Koh, Min-Sung; Rodriguez-Marek, Esteban

doi:10.1109/icassp.2013.6637994

Cited by 7 publications

(27 citation statements)

References 7 publications

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“…Rodriguez-Marek (2013a, 2013b)]. Figure 3 guarantees a perfect reconstruction for any arbitrary EMDFBs, as proved in Koh and Rodriguez-Marek [2013a]. Since Fig.…”

Section: Decimated Memdfbsmentioning

confidence: 81%

“…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.…”

Section: Theory Of Digital Filter Banks Realized Via Memdmentioning

confidence: 99%

“…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.…”

Section: Decimated Memdfbsmentioning

confidence: 99%

“…Since Fig. 3 is extended into decimated MEMDFBs for multichannel data in this paper, we next state the theorem of perfect reconstruction for EMDFBs, where a detailed proof is given in Koh and Rodriguez-Marek [2013a]. Since MEMD has a property of filter banks as shown in Rehman and Mandic [2011], MEMD opens some possibilities to be used as a new filter bank with downsamplings for nonlinear and nonstationary signals.…”

Section: Decimated Memdfbsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Theory of Digital Filter Banks Realized via Multivariate Empirical Mode Decomposition

Koh

Mandic

Constantinides

2014

Adv. Adapt. Data Anal.

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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.

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“…Rodriguez-Marek (2013a, 2013b)]. Figure 3 guarantees a perfect reconstruction for any arbitrary EMDFBs, as proved in Koh and Rodriguez-Marek [2013a]. Since Fig.…”

Section: Decimated Memdfbsmentioning

confidence: 81%

Section: Theory Of Digital Filter Banks Realized Via Memdmentioning

confidence: 99%

Section: Decimated Memdfbsmentioning

confidence: 99%

Section: Decimated Memdfbsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theory of Digital Filter Banks Realized via Multivariate Empirical Mode Decomposition

Koh

Mandic

Constantinides

2014

Adv. Adapt. Data Anal.

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Decimations of intrinsic mode functions via semi-infinite programming based optimal adaptive nonuniform filter bank design approach

et al. 2019

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Computer cryptography through performing chaotic modulation on intrinsic mode functions with non‐dyadic number of encrypted signals

Chen

Ling

Feng

et al. 2019

IET signal process.

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This study proposes a computer cryptographic system through performing the chaotic modulation on the intrinsic mode functions with a non-dyadic number of the encrypted signals. First, the empirical mode decomposition is applied to an input signal to generate a set of intrinsic mode functions. Then, these intrinsic mode functions are categorised into two groups of signals. Next, a type 1 polyphase is employed to represent each group of signals. These polyphase components are combined to generate a non-dyadic number of polyphase components. Second, the chaotic modulation is applied to these combined polyphase components for performing the encryption in the time frequency domain. To reconstruct the original signal, first, the chaotic demodulation is applied to the encrypt components to reconstruct the combined polyphase components. Then, the original groups of intrinsic mode functions are reconstructed through the type 2 polyphase representation and the original signal is reconstructed. Compared with the chaotic filter bank system, the proposed approach enjoys the nonlinear and adaptive property of the empirical mode decomposition. Therefore, a better security performance can be achieved particularly for the non-stationary signals. Compared with the conventional chaotic modulation approach, the proposed system allows performing the cryptography in the time frequency domain.

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Perfect reconstructable decimated two-dimensional empirical mode decomposition filter banks

Cited by 7 publications

References 7 publications

Theory of Digital Filter Banks Realized via Multivariate Empirical Mode Decomposition

Theory of Digital Filter Banks Realized via Multivariate Empirical Mode Decomposition

Decimations of intrinsic mode functions via semi-infinite programming based optimal adaptive nonuniform filter bank design approach

Computer cryptography through performing chaotic modulation on intrinsic mode functions with non‐dyadic number of encrypted signals

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