Performance evaluation of the Hilbert–Huang transform for respiratory sound analysis and its application to continuous adventitious sound characterization

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The use of the Hilbert–Huang transform in the analysis of biomedical signals has increased during the past few years, but its use for respiratory sound (RS) analysis is still limited. The technique includes two steps: empirical mode decomposition (EMD) and instantaneous frequency (IF) estimation. Although the mode mixing (MM) problem of EMD has been widely discussed, this technique continues to be used in many RS analysis algorithms. In this study, we analyzed the MM effect in RS signals recorded from 30 asthmatic patients, and studied the performance of ensemble EMD (EEMD) and noise-assisted multivariate EMD (NA-MEMD) as means for preventing this effect. We propose quantitative parameters for measuring the size, reduction of MM, and residual noise level of each method. These parameters showed that EEMD is a good solution for MM, thus outperforming NA-MEMD. After testing different IF estimators, we propose Kay¿s method to calculate an EEMD-Kay-based Hilbert spectrum that offers high energy concentrations and high time and high frequency resolutions. We also propose an algorithm for the automatic characterization of continuous adventitious sounds (CAS). The tests performed showed that the proposed EEMD-Kay-based Hilbert spectrum makes it possible to determine CAS more precisely than other conventional time-frequency techniques.Postprint (author's final draft

Novel Fourier Quadrature Transforms and Analytic Signal Representations for Nonlinear and Non-stationary Time Series Analysis

The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals in various applications. In this study, like the HT, to obtain quadrature component of a signal, we propose the novel discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine quadrature transforms (FSQTs), designated as Fourier quadrature transforms (FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal (FSAS) representations with following properties: (1) real part of eight FSAS representations is the original signal and imaginary part is the FCQT of the real part, (2) imaginary part of eight FSAS representations is the original signal and real part is the FSQT of the real part, (3) like the GAS, Fourier spectrum of the all FSAS representations has only positive frequencies, however unlike the GAS, the real and imaginary parts of the proposed FSAS representations are not orthogonal to each other. The Fourier decomposition method (FDM) is an adaptive data analysis approach to decompose a signal into a set of small number of Fourier intrinsic band functions which are AM-FM components. This study also proposes a new formulation of the FDM using the discrete cosine transform (DCT) with the GAS and FSAS representations, and demonstrate its efficacy for improved time-frequency-energy representation and analysis of nonlinear and non-stationary time series.Comment: 22 pages, 13 figure

Recent Advances in Theory and Methods for Nonstationary Signal Analysis

Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the very least, everything has a beginning and an end. Thus, while it is necessary to know the theory of stationary processes, one should not adhere to it dogmatically when analyzing data from physical sources, particularly when the observations span an extended period. Nonstationary signals are appropriate models for signals arising in several fields of applications including communications, speech and audio, mechanics, geophysics, climatology, solar and space physics, optics, and biomedical engineering. Nonstationary models account for possible time variations of statistical functions and/or spectral characteristics of signals. Thus, they provide analysis tools more general than the classical Fourier transform for finite-energy signals or the power spectrum for finite-power stationary signals. Nonstationarity, being a “nonproperty” has been analyzed from several different points of view. Several approaches that generalize the traditional concepts of Fourier analysis have been considered, including time-frequency, time-scale, and wavelet analysis, and fractional Fourier and linear canonical transforms

Recent Advances in Theory and Methods for Nonstationary Signal Analysis

Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the very least, everything has a beginning and an end. Thus, while it is necessary to know the theory of stationary processes, one should not adhere to it dogmatically when analyzing data from physical sources, particularly when the observations span an extended period. Nonstationary signals are appropriate models for signals arising in several fields of applications including communications, speech and audio, mechanics, geophysics, climatology, solar and space physics, optics, and biomedical engineering. Nonstationary models account for possible time variations of statistical functions and/or spectral characteristics of signals. Thus, they provide analysis tools more general than the classical Fourier transform for finite-energy signals or the power spectrum for finite-power stationary signals. Nonstationarity, being a “nonproperty” has been analyzed from several different points of view. Several approaches that generalize the traditional concepts of Fourier analysis have been considered, including time-frequency, time-scale, and wavelet analysis, and fractional Fourier and linear canonical transforms

Data-driven Signal Decomposition Approaches: A Comparative Analysis

Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing pipelines, providing useful knowledge and insight into the data and relevant underlying system(s) while also facilitating tasks such as noise or artefact removal and feature extraction. The popular SD methods are mostly data-driven, striving to obtain inherent well-behaved signal components without making many prior assumptions on input data. Among those methods include empirical mode decomposition (EMD) and variants, variational mode decomposition (VMD) and variants, synchrosqueezed transform (SST) and variants and sliding singular spectrum analysis (SSA). With the increasing popularity and utility of these methods in wide-ranging application, it is imperative to gain a better understanding and insight into the operation of these algorithms, evaluate their accuracy with and without noise in input data and gauge their sensitivity against algorithmic parameter changes. In this work, we achieve those tasks through extensive experiments involving carefully designed synthetic and real-life signals. Based on our experimental observations, we comment on the pros and cons of the considered SD algorithms as well as highlighting the best practices, in terms of parameter selection, for the their successful operation. The SD algorithms for both single- and multi-channel (multivariate) data fall within the scope of our work. For multivariate signals, we evaluate the performance of the popular algorithms in terms of fulfilling the mode-alignment property, especially in the presence of noise.Comment: Resubmission with changes in the reference lis