Adaptive Time-frequency Research Articles

Extracting a shape function for a signal with intra-wave frequency modulation.

In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape function could be any smooth 2π-periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that the shape function is a periodic function with respect to its phase function, we can identify certain low-rank structure of the signal. This low-rank structure enables us to extract the shape function from the signal. Once the shape function is obtained, the instantaneous frequency with intra-wave modulation can be recovered from the shape function. We demonstrate the robustness and efficiency of our method by applying it to several synthetic and real signals. One important observation is that this approach is very stable to noise perturbation. By using the shape function approach, we can capture the intra-wave frequency modulation very well even for noise-polluted signals. In comparison, existing methods such as empirical mode decomposition/ensemble empirical mode decomposition seem to have difficulty in capturing the intra-wave modulation when the signal is polluted by noise.

Adaptive Time-Frequency Analysis for Noise Reduction in an Audio Filter Bank With Low Delay

In this paper, an adaptive time-frequency analysis scheme is proposed along with a synthesis scheme using an asymmetric window. The proposed scheme is suitable for audio noise reduction with a low delay in the range of 0 to 4 ms. The main novelty of the paper is the adaptive analysis scheme that can adapt to the incoming signal independently in both time and frequency by employing a complex filter on a DFT modulated filter bank. A number of adaptive time-frequency schemes are described that are suitable for low delay and low computational complexity. The adaptive time-frequency scheme is used for the computation of noise reduction gain factors, which are then adopted in a nonadaptive analysis/synthesis scheme. The synthesis scheme uses an asymmetric window to achieve a good tradeoff between low delay and a sharp frequency response. Examples are given of the adaptive analysis and measurements of the synthesis scheme are given to show that the filter bank has a gain dependent nonlinear phase response. Finally, a noise reduction task is performed that shows good performance compared to reference implementations in terms of segmental SNR and PESQ.

A scalable speech and audio coders based on adaptive time-frequency signal analysis

In the paper is discussed the methods of perceptual sub-band audio signal processing with the dynamic time-frequency map transformation based on the discrete wavelet packet (WP) transform. The advantages of it is that the growing process of WP tree is going from the top to down without returning to smaller scale levels of decomposition and needing to build a complete WP tree, that corresponds to the concept of scalable audio/speech coders implementation in real time. The objective quality assessment of proposed coders based techniques PEMO-Q and comparing with the widespread encoders Opus and Vorbis are given. It shows that the reconstructed signal complies with ITU-R PEAQ at a high compression ratio up to 18 times or more, does not contain artifacts and noise to mask ration less -9 dB.

Element area analysis of chaotic morphology of verical gas-liquid two-phase flow

In order to better understand the variation of flow structure with delay time, we propose the element area (EA) of attractor morphology parameter in this paper. First, the conductance fluctuating signals and adaptive optimal kernel time-frequency representations of different gas-liquid flows are shown, we can find that flow pattern evolution is always accompanied by the numerical and frequency changes of large amplitude fluctuation (LAF). Then three kinds of signals, i. e., rossler signal, white noise and sinusoidal signal with multi-components, are used for analyzing the simulations, and the results indicate that the greater the frequency of LAF, the smaller the delay time of first crest of EA( peak ) is, and that the more the LAF, the bigger the peak value of first crest of EA(hpeak) is. Additionally, we use the above rule to analyze the conductance fluctuating signals measured from upward gas-liquid two-phase flow experiments and the signal length is selected to be 10 s for analysis. When the water superficial velocity is fixed to be 0.1138 m/s and the gas superficial velocity is gradually increased, we find that the peak is constant and hpeak changes up and down at bubble flow. When the flow pattern evolves into bubble-slug transition flow, the peak begins to turn bigger, and when the flow pattern evolves into slug flow, the peak becomes constant again while the hpeak increases monotonically with the gas flow rate increasing. The peak begins to become smaller as the flow pattern evolves from slug flow into churn flow, and we can find that the peak and hpeak of transition flow are alike. The peak and hpeak of bubble flow and churn flow are also alike because their dynamical mechanisms are similar but the downward trend of bubble flow is more gently than that of churn flow. When the water superficial velocity is fixed to be 0.2719 m/s, we can find similar variations of peak and hpeak to the above. Finally we determine the fall ratio (Rf) which is the ratio of the difference between the first crest and the first trough of EA and the hpeak, and then quantitatively distinguish three typical flow patterns, i.e., bubble flow, slug flow and churn flow by the Rf - peak distribution.

Study of the Interference Rejection Based on ATF in DSSS

A novel, adaptive time-frequency interference rejection for suppressing the interference in Direct Sequence Spread Spectrum communication systems is studied in this paper. For a time-localized interference, excision is performed in the time domain. When a frequency domain excision is decided, an adaptive sub-band transform is employed. The most proper sub-spectral split is defined according to the spectrum of the received signal. This joint treatment of time and frequency domains overcomes the performance limitations of the fixed transform-based excision algorithms. The paper presents the performance evaluation of the rejection technique via the analytical and computer simulation tools. It is found that the analytical performance tools match up with the computer simulation results. It is also shown that the proposed adaptive time-frequency interference rejection consistently outperforms the existing interference excision techniques in the literature.

A Fault Feature Extraction Method for Rolling Bearing Based on Pulse Adaptive Time-Frequency Transform

Shock pulse method is a widely used technique for condition monitoring of rolling bearing. However, it may cause erroneous diagnosis in the presence of strong background noise or other shock sources. Aiming at overcoming the shortcoming, a pulse adaptive time-frequency transform method is proposed to extract the fault features of the damaged rolling bearing. The method arranges the rolling bearing shock pulses extracted by shock pulse method in the order of time and takes the reciprocal of the time interval between the pulse at any moment and the other pulse as all instantaneous frequency components in the moment. And then it visually displays the changing rule of each instantaneous frequency after plane transformation of the instantaneous frequency components, realizes the time-frequency transform of shock pulse sequence through time-frequency domain amplitude relevancy processing, and highlights the fault feature frequencies by effective instantaneous frequency extraction, so as to extract the fault features of the damaged rolling bearing. The results of simulation and application show that the proposed method can suppress the noises well, highlight the fault feature frequencies, and avoid erroneous diagnosis, so it is an effective fault feature extraction method for the rolling bearing with high time-frequency resolution.

Robust detection of ionospheric scintillations using MF-DFA technique

The performance of Global Navigation Satellite System (GNSS) receivers is limited by the ionospheric scintillation effects that cause signal degradation due to refraction, reflection and scattering of the signals. Hence, there is a need to develop an ionospheric scintillation detection technique for robust GNSS receivers. In this paper, a new algorithm based on multifractal detrended fluctuation analysis (MF-DFA) is proposed for detecting the ionospheric irregularities. The ionospheric and scintillation GNSS data recorded at Koneru Lakshmaiah (KL) University, Guntur, India, was considered for the analysis. The carrier to noise ratio (C/N 0) time series data of GNSS satellite vehicles that are affected due to scintillations was decomposed using adaptive time–frequency methods like empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD) and complementary ensemble empirical mode decomposition (CEEMD). It was observed that the CEEMD method combined with MF-DFA provides better results as compared to the EMD and EEMD techniques.

Adaptive Time–Frequency Peak Filtering Based on Convex Sets and the Viterbi Algorithm

The time-frequency peak filtering (TFPF) uses the instantaneous frequency estimation technique based on the Wigner-Ville distribution (WVD) to recover signal corrupted by random noise. TFPF is equivalent to a time-invariant low-pass filter whose impulse response is determined by the window function used in windowed WVD. Thus, TFPF cannot track the quick changes of signal, which means that the frequency components of signals higher than some cutoff frequency are attenuated. To solve this problem, we present a novel adaptive algorithm for TFPF. In this algorithm, we first construct the convex set of TFPF estimations at each sample index. Subsequently, we search the optimal estimations from the sequential convex sets to minimize a quadratic functional globally. This leads to a box-constrained convex optimization problem, which can be solved by the Viterbi algorithm. Applications to random seismic noise attenuation have demonstrated the validity of our algorithm with higher output signal-to-noise ratio and less signal information loss than in the traditional TFPF.

Adaptive Optimal Kernel Time–Frequency Representation Technique for Partial Discharge Ultra-high-frequency Signals Classification

An intelligent system for automatic partial discharge pattern recognition is proposed using adaptive optimal kernel time-frequency representation and a fuzzy k-nearest neighbor classifier. The adaptive optimal kernel technique is employed to acquire the joint time-frequency information for partial discharge signals, which is characterized by the adaptive optimal kernel amplitude matrix. A new feature extraction algorithm, i.e., non-negative matrix factorization aided principal component analysis, is proposed to solve the difficulties of principal component analysis for feature extraction of partial discharge adaptive optimal kernel amplitude matrices due to the high dimensionality. Using an ultra-high frequency detector, 600 partial discharge signals sampled from 4 categories of typical artificial defect models in the laboratory are employed for testing. It is shown that the maximum classification accuracy of 94.33% is obtained considering different non-negative matrix factorization parameter r and various non-negative matrix factorization iterations T. Also, the classification performance of the non-negative matrix factorization–principal component analysis features is superior to that of principal component analysis features extracted from original partial discharge signals, two-dimensional non-negative matrix factorization features and phase-resolved partial discharge statistical operators. The proposed technique can be used for partial discharge pattern recognition based on ultra-high-frequency detection arrangements.

Seismic random noise attenuation based on adaptive time–frequency peak filtering

Time–frequency peak filtering (TFPF) method uses a specific window with fixed length to recover band-limited signal in stationary random noise. However, the derivatives of signal such as seismic wavelets may change rapidly in some short time intervals. In this case, TFPF equipped with fixed window length will not provide an optimal solution. In this letter, we present an adaptive version of TFPF for seismic random noise attenuation. In our version, the improved intersection of confidence intervals combined with short-time energy criterion is used to preprocess the noisy signal. And then, we choose an appropriate threshold to divide the noisy signal into signal, buffer and noise. Different optimal window lengths are used in each type of segments. We test the proposed method on both synthetic and field seismic data. The experimental results illustrate that the proposed method makes the degree of amplitude preservation raise more than 10% and signal-to-noise (SNR) improve 2–4dB compared with the original algorithm.

Resolution enhancement of non-stationary seismic data using amplitude-frequency partition

As the Earth's inhomogeneous and viscoelastic properties, seismic signal attenuation we are trying to mitigate is a long-standing problem facing with high-resolution techniques. For addressing such a problem in the fields of time-frequency transform, Gabor transform methods such as atom-window method (AWM) and molecular window method (MWM) have been reported recently. However, we observed that these methods might be much better if we partition the non-stationary seismic data into adaptive stationary segments based on the amplitude and frequency information of the seismic signal. In this study, we present a new method called amplitude-frequency partition (AFP) to implement this process in the time-frequency domain. Cases of a synthetic and field seismic data indicated that the AFP method could partition the non-stationary seismic data into stationary segments approximately, and significantly, a high-resolution result would be achieved by combining the AFP method with conventional spectral-whitening method, which could be considered superior to previous resolution-enhancement methods like time-variant spectral whitening method, the AWM and the MWM as well. This AFP method presented in this study would be an effective resolution-enhancement tool for the non-stationary seismic data in the fields of an adaptive time-frequency transform.

A new time-frequency method to reveal quantum dynamics of atomic hydrogen in intense laser pulses: Synchrosqueezing transform

This study introduces a new adaptive time-frequency (TF) analysis technique, the synchrosqueezing transform (SST), to explore the dynamics of a laser-driven hydrogen atom at an ab initio level, upon which we have demonstrated its versatility as a new viable venue for further exploring quantum dynamics. For a signal composed of oscillatory components which can be characterized by instantaneous frequency, the SST enables rendering the decomposed signal based on the phase information inherited in the linear TF representation with mathematical support. Compared with the classical type of TF methods, the SST clearly depicts several intrinsic quantum dynamical processes such as selection rules, AC Stark effects, and high harmonic generation.

Estimates of the temporal and spatial variability of ocean sound speed on the New Jersey shelf

Estimates of the spatial and temporal variability of ocean sound speed on the New Jersey shelf were obtained using acoustic signals measured by a set of freely drifting buoys. The range- and time-dependent inversion problem is computationally intensive and a linearized perturbative algorithm was applied to obtain results in an efficient manner. The inversion algorithm uses estimates of modal travel time to determine sound speed as a function of range and depth. In order to handle the high volume of data associated with the acoustic sensing network, the modal travel time estimation process was automated using an adaptive time-frequency signal processing method known as time-warping. Time-warping is a model-based transform that converts the frequency-dependent modal arrivals to monotones in the warped domain where they can be easily filtered. The data analyzed in this paper were collected on 16 March 2011 on the New Jersey shelf when the ocean was relatively well-mixed. While the observed sound-speed variations are small, both spatial and temporal trends are observed in the results. Furthermore, the estimated sound-speed profiles show good agreement with temporally and spatially collocated measurements.

Seismic Random Noise Elimination by Adaptive Time-Frequency Peak Filtering

Time-frequency peak filtering (TFPF) with fixed window length effectively attenuates random noise in seismic data, but performs well only for slow-varying seismic signals. To surmount the limitation, we propose the adaptive time-frequency peak filtering with the signal-dependent window length related to the belongings of seismic data to the signal, the signal nonlinearity and the local noise variance. The fuzzy c-means clustering algorithm is used to obtain the belongings in feature space, which incorporates spatial information including local similarity feature, local mean and local median in immediate neighborhood. As a result, the window length is set different for signal and noise and relatively small for the signal with high nonlinearity. We test the proposed method on both synthetic and field seismic data, and our experimental results illustrate that the adaptive method achieves better performance over the conventional TFPF both in random noise attenuation and the effective components preservation.

Spectrogram analysis of frequency-hopping signals based on entropy measure

To analyze and estimate the parameters of Frequency-Hopping(FH) signals effectively,an adaptive time-frequency analytical method was proposed according to the characteristics of FH signal spectrogram and Wigner-Ville Didtribution(WVD).The width of window function for spectrogram was selected based on entropy measure so as to obtain optimal spectrogram representation of FH signal.The theoretical analysis and simulation results show that the spectrum analytical method based on entropy measure could give accurate estimation of the hopping cycle of FH signal under the white Gaussian noise environment of greater than 0 dB.Compared with Smoothed Pseudo WVD(SPWVD) and its adaptive method,the proposed method can effectively reduce the variance and improve the accuracy of parameter estimation at low Signal-to-Noise Ratio(SNR).While for long observation signal,it owns faster operation speed.

The optimal fractional Gabor transform based on the adaptive window function and its application

We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.

Variable short-time Fourier transform for vibration signals with transients

This paper presents a fast adaptive time-frequency method for analyzing stationary and nonstationary vibration signals with transients. The method is developed based on instantaneous frequency (IF) – variations in the time domain. The variable window length is determined by estimating the local IF in every window slice over time. The proposed method is tested using simulation signals and experimental vibration data. The results show that the proposed method can successfully retrieve transient signals at a 3 dB signal-to-noise ratio, and improve stationary and nonstationary signal resolution in time and frequency domains. The proposed scheme offers better resolution compared to the standard short-time Fourier transform (STFT), and the computing cost is only slightly greater than STFT scheme.

Ensemble Noise-Reconstructed Empirical Mode Decomposition for Mechanical Fault Detection

Various faults inevitably occur in mechanical systems and may result in unexpected failures. Hence, fault detection is critical to reduce unscheduled downtime and costly breakdowns. Empirical mode decomposition (EMD) is an adaptive time-frequency domain signal processing method, potentially suitable for nonstationary and/or nonlinear processes. However, the EMD method suffers from several problems such as mode mixing, defined as intrinsic mode functions (IMFs) with incorrect scales. In this paper, an ensemble noise-reconstructed EMD method is proposed to ameliorate the mode mixing problem and denoise IMFs for enhancing fault signatures. The proposed method defines the IMF components as an ensemble mean of EMD trials, where each trial is obtained by sifting signals that have been reconstructed using the estimated noise present in the measured signal. Unlike traditional denoising methods, the noise inherent in the input data is reconstructed and used to reduce the background noise. Furthermore, the reconstructed noise helps to project different scales of the signal onto their corresponding IMFs, instrumental in alleviating the mode mixing problem. Two critical issues concerned in the method, i.e., the noise estimation strategy and the number of EMD trials required for denoising are discussed. Furthermore, a comprehensive noise-assisted EMD method is proposed, which includes the proposed method and ensemble EMD (EEMD). Numerical simulations and experimental case studies on accelerometer data collected from an industrial shaving process are used to demonstrate and validate the proposed method. Results show that the proposed method can both detect impending faults and isolate multiple faults. Hence, the proposed method can act as a promising tool for mechanical fault detection.

Time–frequency analysis for parametric and non-parametric identification of nonlinear dynamical systems

This paper points out the differences between linear and nonlinear system identification tasks, shows that time–frequency analysis is most appropriate for nonlinearity identification, and presents advanced signal processing techniques that combine time–frequency decomposition and perturbation methods for parametric and non-parametric identification of nonlinear dynamical systems. Hilbert–Huang transform (HHT) is a recent data-driven adaptive time–frequency analysis technique that combines the use of empirical mode decomposition (EMD) and Hilbert transform (HT). Because EMD does not use predetermined basis functions and function orthogonality for component extraction, HHT provides more concise component decomposition and more accurate time–frequency analysis than the short-time Fourier transform and wavelet transform for extraction of system characteristics and nonlinearities. However, HHT's accuracy seriously suffers from the end effect caused by the discontinuity-induced Gibbs' phenomenon. Moreover, because HHT requires a long set of data obtained by high-frequency sampling, it is not appropriate for online frequency tracking. This paper presents a conjugate-pair decomposition (CPD) method that requires only a few recent data points sampled at a low-frequency for sliding-window point-by-point adaptive time–frequency analysis and can be used for online frequency tracking. To improve adaptive time–frequency analysis, a methodology is developed by combining EMD and CPD for noise filtering in the time domain, reducing the end effect, and dissolving other mathematical and numerical problems in time–frequency analysis. For parametric identification of a nonlinear system, the methodology processes one steady-state response and/or one free damped transient response and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. For non-parametric identification, the methodology uses the maximum displacement states to determine the displacement–stiffness curve and the maximum velocity states to determine the velocity–damping curve. Numerical simulations and experimental verifications of several nonlinear discrete and continuous systems show that the proposed methodology can provide accurate parametric and non-parametric identifications of different nonlinear dynamical systems.

Detecting unstable periodic orbits from oil-gas-water three-phase slug flows

We use the close return method combined with adaptive threshold selection to detect the unstable periodic orbits from the signals measured from experimental oil-gas-water three-phase slug flows, and find that the period of the emulsion type slug flow is longer than that of oil in water type slug flow. Especially, the orbit of oil in water type slug flow is basically composed of one big loop and one small loop, and the emulsion type slug flow orbit is composed of two big smooth loops. In addition, we employ the method of adaptive optimal kernel time-frequency representation to investigate the flow behaviors of two typical oil-gas-water three-phase slug flows and indicate that the energy of the oil in water slug flow exhibits a dispersed distribution and its frequency spectrum consists of various components distributes in a wide range. In contrast, the energy of emulsion type slug flow is distributed in a rather concentrated region and the high frequency component in its frequency spectrum is much less than that of the oil in water slug flow. These results are well consistent with the detected structure of unstable periodic orbit, further suggesting that the fluid mechanism underlying oil in water type slug flow is more complicated than that of the emulsion type slug flow.