Instantaneous Frequency Calculation for Intrinsic Mode Functions Based on High-order Ambiguity Function

Each year 400,000 North Americans die from sudden cardiac death (SCD). T- wave alternans (TWA) refers to an alternating pattern in the T-wave portion of the surface electrocardiogram (ECG) and has been shown as a risk stratifier for SCD. These subtle changes in the T-waves are in the micro-volt scale and ambulatory ECG recordings usually contain biological noise. Also, data non-stationarity owing to heart rate variability and the amplitude variability in TWA magnitude can limit the accuracy of the detection techniques. This necessitates the need for robust detection algorithms for processing such non-stationary data. In this thesis, we have proposed an Empirical Mode Decomposition (EMD) based scheme combined with the Instantaneous Frequency (IF). EMD decomposes the signal into several monocomponent signals called Intrinsic Mode Functions (IMFs). IF extracted from these IMFs provides an accurate estimate of time varying frequency components and hence can aid during characterization of TWAs. In order to validate the performance of the proposed detection technique, the feature vectors extracted from the IMFs were fed to a linear discriminant analysis (LDA) classifier. The performance assessment was carried out using two datasets: (a) Synthetic TWAs: 72 signals obtained from publicly accessible Physionet database and (b) TWAs from patients: 55 ambulatory ECG signals obtained from the Toronto General Hospital. Using an unbiased leave-one-out cross validation strategy, maximum overall classification accuracies of 86.1% and 81.8% were achieved for TWA detection from synthetic and ambulatory ECG recordings respectively. In addition, the usability of the proposed technique has been investigated to assess its suitability for addressing another cardiovascular problem stroke. Atrial Fibrillation (AF) has been identified as a risk factor to increase the chances of stroke. The most common method in studying the complex AF electrograms is to employ dominant frequency (DF) analysis; however, due to signal non-stationarity DF does not always provide the best estimate of the atrial activation rate. As a result, analyzing the electrograms via EMD and IF has been investigated as the second contribution of this work.

This paper considers the parameter estimation of multicomponent polynomial-phase signals (mc-PPSs) with orders greater than two. The proposed method combines the product cubic phase function (PCPF) and high-order ambiguity function (HAF) when the mc-PPS orders exceed three. In the proposed method, the HAF is first applied to the observed mc-PPS to produce a cubic phase signal. Second, the algorithm is modified to estimate the parameters of mc-PPS using the CPF. To obtain accurate estimates of the two highest-order parameters (i.e., $$ a_{P} $$ and $$ a_{P - 1} $$ of each component), all possible $$ a_{P} $$ and $$ a_{P - 1} $$ must be obtained in this step in all combinations of the instantaneous frequencies; then, the maximum absolute value of all sum values must be identified by dechirping with all possible $$ a_{P} $$ and $$ a_{P - 1} $$ . In addition, non-uniformly-spaced signal sample methods are used to employ fast Fourier transformation in the CPF. The proposed method is different from the PCPF–HAF method proposed by other researchers; it is referred to as the improved PCPF–HAF method and can remedy the shortcomings of the traditional method when estimating mc-PPS parameters. Additionally, the PCPF–HAF method cannot be used to treat multicomponent third-order polynomial-phase signals, but the proposed method can treat them using non-uniformly-spaced signal sample methods. The cross-terms can also be restrained more effectively than with the CPF, resulting in higher accuracy of the estimated parameters and a lower signal-to noise ratio threshold. Theoretical analysis and simulations are presented to support these claims.

This paper makes use of local polynomial Wigner-Ville distribution (LPWVD), originally designed for nonparametric instantaneous frequency (IF) estimation of transient signals, to propose a parametric IF estimation for polynomial phase signals (PPSs). Statistical performance such as asymptotic bias and variance of the LPWVD-based parametric IF estimator is derived in closed-form. Based on the analytical results, we extend the statistical efficiency of the Wigner-Ville distribution (WVD) for a second-order PPS only to that of the LP-WVD for an arbitrary order, when the IF is estimated at the middle of sample observations. Simulation results verify the analytical performance and comparisons with the polynomial Wigner-Ville distribution (PWVD) show that the LPWVD-based parametric IF estimator can provide better performance.

Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can monitor the DoA by observing the patient’s electroencephalography (EEG) signals during the surgical procedure. Typically high frequency EEG signals indicates the patient is conscious, while low frequency signals mean the patient is in a general anaesthetic state. If the anaesthetist is able to observe the instantaneous frequency changes of the patient’s EEG signals during surgery this can help to better regulate and monitor DoA, reducing surgical and post-operative risks. This paper describes an approach towards the development of a 3D real-time visualization application which can show the instantaneous frequency and instantaneous amplitude of EEG simultaneously by using empirical mode decomposition (EMD) and the Hilbert–Huang transform (HHT). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMFs). The Hilbert spectral analysis method is then used to obtain instantaneous frequency data. The HHT provides a new method of analyzing non-stationary and nonlinear time series data. We investigate this approach by analyzing EEG data collected from patients undergoing surgical procedures. The results show that the EEG differences between three distinct surgical stages computed by using sample entropy (SampEn) are consistent with the expected differences between these stages based on the bispectral index (BIS), which has been shown to be quantifiable measure of the effect of anaesthetics on the central nervous system. Also, the proposed filtering approach is more effective compared to the standard filtering method in filtering out signal noise resulting in more consistent results than those provided by the BIS. The proposed approach is therefore able to distinguish between key operational stages related to DoA, which is consistent with the clinical observations. SampEn can also be viewed as a useful index for evaluating and monitoring the DoA of a patient when used in combination with this approach.

Currently, empirical mode decomposition (EMD) has become a popular data-driven time-frequency analysis method for nonstationary and nonlinear data. However, it is still limited to univariate data due to the number and/or scale misalignment for multivariate data. A newly developed multivariate EMD (MEMD) scheme decomposes multivariate data simultaneously and thus leads to mode alignment and minimizes mode mixing. In addition, an improved amplitude and frequency modulation (AM-FM) decomposition algorithm presented here provides an estimation of a more meaningful instantaneous amplitude and frequency than the widely used Hilbert transform (HT). Both of these facilitate development of a time-frequency analysis framework for multivariate nonstationary and nonlinear data analysis. In this paper, MEMD-based scalogram and coscalogram, and instantaneous frequency spectra and cospectra are proposed to characterize a multivariate nonstationary process. The scalogram and instantaneous frequency spectra capture spectral evolution of each component while the coscalogram and instantaneous frequency cospectra reveal embedded intermittent correlation between two components. Compared with scale-based scalogram and coscalogram, frequency-based instantaneous frequency spectra and cospectra provide a more detailed portrait of multivariate data. The effectiveness of the proposed MEMD-based time-frequency analysis framework is demonstrated by numerical examples of a thunderstorm downburst and an earthquake ground motion. Also, the results from the MEMD-based approach are compared with those based on a continuous wavelet transform, which further reinforces the effectiveness of the proposed framework.

Cepstral features and their derivatives have been successfully used in speaker recognitions tasks over the past two decades. Recently new features are emerging that make use of information that is not contained in cepstral features or their derivative, namely the phase spectra and instantaneous frequency. There are numerous approaches to capture instantaneous amplitude and frequency variations in the signal, resulting in an amplitude and frequency modulation (AM-FM) feature set. While the addition of modulation features has been shown to improve speech recognition systems based on cepstral features, their use in speaker recognition is new and has not been fully explored. This paper outlines some of these emerging features and their extraction methods for use in speaker recognition tasks. The paper also talks about the recently proposed Empirical Mode Decomposition (EMD) as an alternative method of extracting instantaneous frequency.

Near-infrared spectroscopy (NIRS) can be used as the basis of non-invasive neuroimaging that may allow the measurement of haemodynamic changes in the human brain evoked by applied stimuli. Since this technique is very sensitive, physiological interference arising from the cardiac cycle and breathing can significantly affect the signal quality. Such interference is difficult to remove by conventional techniques because it occurs not only in the extracerebral layer but also in the brain tissue itself. Previous work on this problem employing temporal filtering, spatial filtering, and adaptive filtering have exhibited good performance for recovering brain activity data in evoked response studies. However, in this study, we present a time-frequency adaptive method for physiological interference reduction based on the combination of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). Monte Carlo simulations based on a five-layered slab model of a human adult head were implemented to evaluate our methodology. We applied an EMD algorithm to decompose the NIRS time series derived from Monte Carlo simulations into a series of intrinsic mode functions (IMFs). In order to identify the IMFs associated with symmetric interference, the extracted components were then Hilbert transformed from which the instantaneous frequencies could be acquired. By reconstructing the NIRS signal by properly selecting IMFs, we determined that the evoked brain response is effectively filtered out with even higher signal-to-noise ratio (SNR). The results obtained demonstrated that EMD, combined with HSA, can effectively separate, identify and remove the contamination from the evoked brain response obtained with NIRS using a simple single source–detector pair.

This paper presents an Empirical mode decomposition (EMD) approach for achieving high-speed frequency-tagged steady state visual evoked potential (SSVEP) brain computer interface (BCI) system. Empirical mode decomposition (EMD) has been demonstrated as a local and fully data-driven technique for the data processing of nonlinear and non-stationary time-series. It allows the frequency and amplitude of a time-series to be evaluated with excellent time resolution. The proposed system utilized flickering sources with high flickering rate acting as cursor system for the purpose of alternatively communication system. Induced EEG signal were decomposed into different scale of oscillation components namely intrinsic mode functions. In order to find out the SSVEP-related IMFs, instantaneous frequency were computed by generalized zero crossing (GZC). After identification of the frequency power by quadrature detection, the result shows the proposed system achieved 51.46 bits/min of average ITR. Compare with FFT approaches, EMD method provide better temporal and frequency sensitivity in detection of cognitive state of neuron activities.KeywordsBrain computer interface (BCI)Empirical mode decomposition (EMD)Steady-state visual evoked potential (SSVEP)

Phase estimation plays an important role in various signal processing areas like Radar, Sonar, power systems, speech analysis, communications and many others. The phase of the analytic form of the non stationary signals can be used to find instantaneous frequency. This paper addresses the problem of simultaneous phase and instantaneous frequency estimation from polynomial phase signals embedded in Gaussian noise. Here we have introduced the modified signal tracking approach which is then realized using unscented Kalman filter. The state space model is derived using Taylor series expansion of the phase of polynomial phase signal as process model while Polar to Cartesian conversion as measurement model. Proposed method, compared with state-of-the-art, performs better for signals with higher order polynomial phase variations at lower Signal-to-Noise-Ratio (0-5dB). We also present the simulation results for phase estimation.

In this work, a new instantaneous fundamental frequency extraction method is presented, with the attention especially focused on its robustness for pathological voices processing. It is based on the Ensemble Empirical Mode Decomposition (EEMD) algorithm, which is a completely data-driven method for signal decomposition into a sum of AM - FM components, called Intrinsic Mode Functions (IMFs) or modes. Our results show that the speech fundamental frequency can be captured in a single IMF. We also propose an algorithm for selecting the mode where the fundamental frequency can be found, based on the logarithm of the power of the IMFs. The instantaneous frequency is then extracted by means of well-known techniques. The behaviour of the proposed method is compared with other two ones (Robust Algorithm for Pitch Tracking -RAPT- and auto-correlation based algorithms), both in normal and pathological sustained vowels.

Beam damage detection using synchronisation of peaks in instantaneous frequency and amplitude of vibration data

Borehole Radar (BHR) uses ultra-wideband electromagnetic (EM) waves to image discontinuities in formations. It has been a major bottleneck to extend BHR applications to obtain a clear and high-resolution radar profile in a complex and noisy environment, which increases ambiguity in the geology interpretation. To avoid this increased ambiguity in the geology interpretation, we proposed a scheme based on the empirical mode decomposition (EMD) and complex signal analysis theory to process the BHR data with low signal to noise ratio (SNR). The scheme includes four steps. First, the original radar profile is pre-processed to avoid mode confusion and noise interference to the radar echo. Next, the EMD method is used to process a single-channel radar dataset and to analyze the frequency components of the radar signal. Various intrinsic modes of the pre-processing radar profile are also obtained by using EMD. Finally, we reconstruct the intrinsic mode profile, which contains information about the formation, calculate the complex signals of the reconstructed radar profile using the Hilbert transform, extract the three instantaneous attributes (instantaneous amplitude, instantaneous phase, and instantaneous frequency), and draw the separate instantaneous attributes profiles. This processing scheme provides both the conventional time-distance profile also in addition to the three instantaneous attributes. The additional attributes reduce ambiguity when evaluating the original radar profile and avoid the deviation relying solely on a conventional time-distance profile. An actual radar profile, which was obtained by a BHR system in a limestone fracture zone, is used to verify the effectiveness of instantaneous attributes for improving interpretation accuracy. The results demonstrate that the EMD method is superior in processing the BHR signal under a low SNR and has the capability to separate the high-low components of the radar echo effectively.

Model selection of the generalized von Mises distribution based on empirical mode decomposition with data analyses

Novel and efficient computation of Hilbert–Huang transform on surfaces

Instantaneous frequency estimation for wheelset bearings weak fault signals using second-order synchrosqueezing S-transform with optimally weighted sliding window