Instantaneous Frequency Distribution Research Articles

Phase tracking using a Kalman filter based on probability density distribution in frequency-scanning interferometry

Frequency-scanning interferometry (FSI) utilizing external cavity diode lasers (ECDL) stands out as a potent technique for absolute distance measurement. Nevertheless, the inherent scanning nonlinearity of ECDL and phase noise pose a challenge, as it can compromise the accuracy of phase extraction from interference signals, thereby reducing the measurement accuracy of FSI. In this study, we propose a composite algorithm aimed at mitigating non-orthogonal errors by integrating the least-squares and Heydemann correction technique. Furthermore, we employ Kalman filtering for precise phase tracking. We introduce a parameter selection strategy based on the statistical distribution of instantaneous frequency to achieve the fusion estimation of phase observation values and theoretical models, which starts a new perspective for the application of multi-dimensional data fusion in FSI measurement. Through simulation and experimental validation, the efficacy of this approach is confirmed. The experimental results show promising outcomes: with an average phase error of 0.12%, a standard deviation of less than 1.7 µm in absolute distance measurement, and an average positioning accuracy error of 0.29 µm.

Dynamic Characteristics of State Transitions Composed of Neural Activity in the Brain by Circadian Rhythms.

In recent years, as a treatment for mental disorders in addition to drug treatment, a non-drug treatment called chronotherapy has been attracting attention. However, the achievement of optimized chronotherapy for each subject's condition requires that the disturbance of the patient's circadian rhythm must be captured over a long duration. Therefore, it is necessary to develop biomarkers that are easy to measure, quantitative, and continuously measured. Complexity analysis of electroencephalograms revealed specific patterns related to circadian rhythms. However, such complexity analysis cannot capture variability in spatial patterns, although moment-to-moment temporal dynamic characteristics can be captured. Therefore, it is necessary to evaluate the dynamic characteristics of the interaction of neural activity throughout the brain. To evaluate the dynamic whole-brain interaction, we proposed a new microstate approach based on the instantaneous frequency distribution. In this context, we hypothesized that it would be possible to detect circadian rhythms using the microstate approach. In this study, to clarify the dynamic interactions of the entire neural network of the brain by circadian rhythms, we measured EEG data at day and night, and detected dynamic state transitions based on the instantaneous frequency distribution of the whole brain from EEG. The results showed the probability of transition among region-specific phase-leading states related to circadian rhythms. This finding might be widely utilized to detect circadian rhythms in healthy and pathological conditions.

Model-Free Lens Distortion Correction Based on Phase Analysis of Fringe-Patterns.

The existing lens correction methods deal with the distortion correction by one or more specific image distortion models. However, distortion determination may fail when an unsuitable model is used. So, methods based on the distortion model would have some drawbacks. A model-free lens distortion correction based on the phase analysis of fringe-patterns is proposed in this paper. Firstly, the mathematical relationship of the distortion displacement and the modulated phase of the sinusoidal fringe-pattern are established in theory. By the phase demodulation analysis of the fringe-pattern, the distortion displacement map can be determined point by point for the whole distorted image. So, the image correction is achieved according to the distortion displacement map by a model-free approach. Furthermore, the distortion center, which is important in obtaining an optimal result, is measured by the instantaneous frequency distribution according to the character of distortion automatically. Numerical simulation and experiments performed by a wide-angle lens are carried out to validate the method.

Instantaneous frequencies in the Kuramoto model.

Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical description of the instantaneous frequency (phase-velocity) distribution. Our result is validated against numerical simulations, and we illustrate it in cases in which the natural frequencies have normal and Beta distributions. In both cases, we vary the coupling strength and compare systematically the distribution of time-averaged frequencies (a known result of Kuramoto theory) to that of instantaneous frequencies, focusing on their qualitative differences near the synchronized frequency and in their tails. For a class of natural frequency distributions with power-law tails, which includes the Cauchy-Lorentz distribution, we analyze the tails of the instantaneous frequency distribution by means of an asymptotic formula obtained from a power-series expansion.

Instantaneous Respiratory Response of Gamer with High-Risk Internet Gaming Disorder during Game-Film Stimuli by Using Complementary Ensemble Empirical Mode Decomposition.

Gamers with Internet gaming disorder (IGD) dynamically regulate their psychophysiological responses during playing; however, analyzing instantaneous psychophysiological responses in these gamers has been limited by a lack of appropriate methods. We propose combining the Complementary Ensemble Empirical Mode Decomposition and Direct Quadrature methods to overcome this limitation. The related effect of abdominal breathing (AB) training (as a relaxing psychology method) on the distribution of instantaneous frequency (IF) was investigated by calculating median (IFmed), kurtosis (IFkurt) and skewness (IFskew), and 19 participants with high-risk IGD (HIGD) were found to have increased IFmed [massively multiplayer online role-playing game (MMORPG): 0.36 ± 0.08; first-person shooter game (FPSG): 0.34 ± 0.08] but decreased IFkurt (MMORPG: 5.98 ± 2.31; FPSG: 6.84 ± 4.61) and IFskew (MMORPG: 0.40 ± 0.69; FPSG: 0.64 ±1.04) during game-film stimuli compared with baseline and recovery states. After AB training, IFmed of these 19 participants (MMORPG: 0.24 ± 0.11; FPSG: 0.18 ± 0.06) decreased significantly. This study is firstly to observe the IF distribution of respiratory signal in gamers with HIGD; thus, this distribution may be used as a respiratory physiological marker of IGD risk.

A Demodulation Model of Dynamic Low-Finesse Fabry-Perot Cavity Based on the Instantaneous Frequency

If the measurand changes during the spectrum acquisition process, it easily leads to the failure of the classic demodulation algorithms of low-finesse optical fiber Fabry-Perot (FP) sensors. To address this problem, a novel demodulation model is proposed based on the definition of the instantaneous frequency. The proposed model establishes the relationship between the optical path length (OPL) of the FP cavity and the instantaneous frequency distribution of the FP interference spectrum. The link between the classic FFT algorithm and this model is discussed, and it is found that this model can be viewed as a generalized form of the FFT algorithm. Based on this model, the Doppler-induced demodulation error is analyzed. The analysis uncovers that the average frequency of the FP interference spectrum should be used for the evaluation of the error, and the error is proportional to the variation of OPL during the spectrum acquisition period. Further, numerical simulation and an experiment were carried out to verify the proposed model, and results show that the proposed model is effective for the dynamic low-finesse FP cavity. It is the first time that the idea of instantaneous frequency is introduced for the FP demodulation, and this model provides us a new way to cope with the FP sensing signal.

An instantaneous frequency analysis method of stay cables

This paper presents and evaluates in detail a conjugate-pair decomposition method for tracking the instantaneous frequency of a vibration signal by processing only three (or more) most recent data points, and Probability Box theory was employed to obtain the uncertain probability distribution of instantaneous frequency. A composite cable-stayed bridge with large span, named as Guanhe Bridge, was selected as the engineering background; the proposed conjugate-pair decomposition method is verified and compared with Hilbert–Huang transform method using the measured dynamical data of structural health monitoring system. Moreover, the uncertain probability distribution of instantaneous frequency was discussed; the Probability Box also can be obtained. Results show that the identify results are close to each other using conjugate-pair decomposition and Hilbert–Huang transform, respectively; but the variance of conjugate-pair decomposition is less than Hilbert–Huang transform, and conjugate-pair decomposition requires only a few data points for sliding-window fitting to extract the instantaneous frequency, and the Probability Box of instantaneous frequency will be useful to evaluate safety and potential fatigue problems in the bridge cables.

Application of SN-EMD in Mode Feature Extraction of Ship Radiated Noise

Due to the randomness of added noise, noise-assisted versions based on EMD (empirical mode decomposition) usually cause new “mode mixing” problem. In addition, these algorithms also have problems such as high time-consuming and large recovering error. For the reasons, a new method SN-EMD (Selective Noise-assisted EMD) is put forward in this paper. It determines whether to add noise as assistance by judging whether there is high frequency intermittent component contained in the signal or not. The new method was proved to have the optimal performance by comparing the performance parameters for evaluating the decomposition. In this paper, SN-EMD was used to decompose ship radiated noise. On account of the differences in the original information contained in each mode of radiated noise signals from different ship, we selected the first three modes for processing. Average instantaneous frequency, center frequency, energy density, and energy distribution ratio were extracted as mode feature of ship targets for classification and recognition. Spatial distribution of the feature quantities in three-dimensional space verified similarity of the same target and separability of different targets.

Multiscale modeling of fiber optic gyroscope temperature drift based on improved ensemble empirical mode decomposition.

Temperature drift is a major error source of the fiber optic gyroscope (FOG), and the method of modeling is important in eliminating it. A method of multiscale modeling based on improved ensemble empirical mode decomposition (EEMD) is proposed in this paper. First, in order to improve the ability of eliminating mode mixing, the influence of the frequency of the masking signal on mode mixing is analyzed. Then we conclude that the frequency of the masking signal should be higher than that of the signal, and an improved EEMD is proposed based on the conclusion. Second, the temperature drift of FOG is filtered by applying the permutation entropy to the intrinsic mode functions (IMFs). Third, the IMFs are divided into several scales according to the mean value and the distribution of instantaneous frequency of IMFs. Finally, the algorithm of the support vector machine is used to model each scale, and the models are accumulated into a total model. The regression error after compensation of the proposed method (in the case of the mean squared error indicator) increased by more than two orders of magnitude compared to the original temperature drift.

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition.

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Morphodynamic Profiling of Cell Protrusion Based on Spatiotemporal Spectrum Decomposition and Unsupervised Clustering

Cellular morphogenesis is governed and regulated by complex interactions between the cytoskeleton and molecular pathways. Due to their central roles in the differentiation, embryogenesis and homeostasis process, cell morphology and morphodynamics are often used for qualitative and quantitative assessments of cell state. Here, we propose a framework to quantitatively profile cellular morphodynamics based on an adaptive spectrum decomposition method. This method decomposes the motion of cell boundary into analytical instantaneous frequency spectrum through Hilbert-Huang transform (HHT). Subsequently, we computed for each decomposed signal the distribution of instantaneous frequency and amplitude, from which we compiled the HHT spectrum. For spontaneously protrusive Cos7 cells, the instantaneous magnitudes of protrusion were found to greatly vary across different cells with nearly identical genetic and molecular backgrounds, whereas the frequency spectra were remarkably consistent. Meanwhile we examined Cos7 cells in which the Vav2 Guanine Exchange Factor (GEF) activity was acutely perturbed by optogenetic tools, and found significant shifts in the frequency distribution for specific signals. We thus concluded that edge motion velocity is an arbitrary parameter of cell morphogenesis whereas the frequency spectrum encodes the molecular state of regulation. The features extracted from the HHT spectrum could be used as a classifier to group subcellular regions into numerous characteristic sectors with specific molecular states through Statistical Region Merging (SRM) based clustering. Finally, we monitored the Rac1 activity downstream of Vav2 expressed in Cos7 cells and found that those clustering sectors distinguished by morphodynamic parameters indeed reflect regions with different local signaling. Thus, cell morphodynamic behavior can be used to detect different modes of operations or perturbations in cellular signaling.

Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function (IFDF) to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse time-frequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

Instantaneous frequency distribution for pulse-output DDS

The pulse-output Direct Digital Synthesis (DDS), in which the overflow signal of the phase accumulator is used for the pulse output, can be applied to sonar and radar systems as a way of signal generation and modulation. Despite its simple hardware implementation, it suffers the drawback of phase jitter. In this paper, the pulse-output DDS for continuous wave (CW) signal generation is introduced and the phase jitter problem is analysed. By examining the instantaneous frequency of the overflow signal, this paper reveals that the generated CW pulse is far from being single frequency, instead two different frequencies exist. How these two frequency components are distributed with time is also considered. An inequality that helps select the value of system clock to achieve certain frequency precision is given. This paper also analyses the pulse duration error and initial time delay error. Experiment results are in good agreement with calculations.

A New Method for Fusion of Measured and Model-derived Solar Radiation Time-series

When planning solar plants project developers and financers consider the long-term average of solar radiation and its uncertainty as the most important site selection criteria. Accurate time series of at least 10 years length are needed to calculate realistic estimates of such long-term averages. Ground-based measurements usually are not available for long time periods, but satellite- derived data may show significant differences compared to more accurate ground-measured values with respect to instantaneous values and frequency distribution. To overcome these shortcomings a new method for adaption of satellite-derived solar radiation values to ground measured time-series is developed. One year of overlapping time period is used for training the adaption. A weighted polynomial fit with additional constraints is then applied to the remaining satellite-derived solar radiation values. The method is tested at two sites for four satellite data models. The results show improvements for all data sets. After applying the adaption also during periods where no ground-based measurements are available the bias on average is nearing 0% for most models. This requires that the satellite-derived data realistically represent the interannual variability. Frequency distributions are also matching better. Especially this is the case for maxima, which can be critical for design purposes.

Improvement of the HHT method and application in weak vortex signal detection

The vortex signal is greatly disturbed by noises from external interference when the meter works at low flow rate, which results in a limited measuring range for the flowmeter. In order to solve the problem, a new signal processing method based on the Hilbert–Huang transform (HHT) is proposed. With its good performance on local adaptability and time–frequency analysis, noises are removed by the empirical mode decomposition (EMD) and the residue components are analysed by the Hilbert transform; then instantaneous frequency distributions are achieved. When the probability density of a certain frequency component exceeds 5%, the sifting process will be terminated. Subsequently, the vortex frequency can be calculated from the last residue component. Experimental studies were carried out to compare the improved method with the classic method FFT at low flow rate. A better linearity and lower limit of measurement are achieved by the proposed method.

Phase effects in F0 discrimination and temporal fine structure

Pitch discrimination with only high-order (unresolved) harmonics is dependent on their relative phases and is thought to be based on the temporal envelope of the waveform after peripheral filtering. In contrast, when low-order harmonics are present, phase effects disappear, and pitch may be derived from the estimated frequencies of the individual resolved harmonics. The dichotomy between the envelope-based periodicity from unresolved harmonics and the temporal fine-structure (or spectrally) based estimates of individual frequencies from resolved harmonics forms the basis of the well-known two-mechanism theory of pitch. Recently, the early idea that listeners use temporal fine-structure cues in unresolved harmonics to estimate the overall F0 has been revived as a third intermediate mechanism to account for why accurate F0 discrimination, normally associated with resolved harmonics, can sometimes be achieved in conditions that produce phase effects. Here we show that it is not necessary to resort to a third mechanism. Instead, we show that the relative component phases affect the instantaneous frequency distributions in ways that could influence the coding of frequencies for individual, partially resolved, harmonics. Implications for the interpretation of temporal fine structure in pitch and other auditory functions, such as speech perception, are discussed. [Work supported by NIH R01DC05216.]

Time-frequency characterization of atrial fibrillation from surface ECG based on Hilbert-Huang transform

In this paper, based on Hilbert-Huang transform (HHT), we develop a new non-invasive time-frequency analysis method to characterize the dynamic behaviour of atrial fibrillation (AF) from surface ECG. We first extract f waves from single-lead ECG records of AF patients using PCA analysis. To capture the non-stationary behaviours of AF signals at different time scales, we use HHT to find the Hilbert spectrum and instantaneous frequency (IF) distribution of residual signals from principal component analysis. Two important feature variables, namely mean IF (mIF) and index of frequency stability over time (IS), are derived from the IF distribution, and in combination will be able to effectively discriminate two different AF types: self-terminating and non-terminating termination. The proposed AF signal decomposition and analysis method will help us efficiently differentiate individual AF patients, advance our understanding of AF mechanisms, and provide useful guidelines for improving administration of AF patients, especially paroxysmal AF.

Short-time phase spectrum in speech processing: A review and some experimental results

Incorporating information from the short-time phase spectrum into a feature set for automatic speech recognition (ASR) may possibly serve to improve recognition accuracy. Currently, however, it is common practice to discard this information in favour of features that are derived purely from the short-time magnitude spectrum. There are two reasons for this: (1) the results of some well-known human listening experiments have indicated that the short-time phase spectrum conveys a negligible amount of intelligibility at the small window durations of 20–40 ms used for ASR spectral analysis, and (2) using the short-time phase spectrum directly for ASR has proven difficult from a signal processing viewpoint, due to phase-wrapping and other problems. In this article, we explore the possibility of using short-time phase spectrum information for ASR by considering the two points mentioned above. To address the first point, we review the results of our own set of human listening experiments. Contrary to previous studies, our results indicate that the short-time phase spectrum can indeed contribute significantly to speech intelligibility over small window durations of 20–40 ms. Also, the results of these listening experiments, in addition to some ASR experiments, indicate that at least part of this intelligibility may be supplementary to that provided by the short-time magnitude spectrum. To address the second point (i.e., the signal processing difficulties), we suggest that it may be necessary to transform the short-time phase spectrum into a more physically meaningful representation from which useful features could possibly be extracted. Specifically, we investigate the frequency-derivative (or group delay function, GDF) and the time-derivative (or instantaneous frequency distribution, IFD) as potential candidates for this intermediate representation. We review our recent work, where we have performed various experiments which show that the GDF and IFD may be useful for ASR. In our recent work, we have also conducted several ASR experiments to test a feature set derived from the GDF. We found that, in most cases, these features perform worse than the standard MFCC features. Therefore, we suggest that a short-time phase spectrum feature set may ultimately be derived from a concatenation of information from both the GDF and IFD representations. For best performance, the feature set may also need to be concatenated with short-time magnitude spectrum information. Further to addressing the two aforementioned points, we also discuss a number of other speech applications in which the short-time phase spectrum has proven to be very useful. We believe that an appreciation for how the short-time phase spectrum has been used for other tasks, in addition to the results of our own experiments, will provoke fellow researchers to also investigate its potential for use in ASR.

Further intelligibility results from human listening tests using the short-time phase spectrum

State-of-the-art automatic speech recognition systems (ASRs) use only the short-time magnitude spectrum for feature extraction; the short-time phase spectrum is generally ignored in these systems. Results from our recent human listening tests indicate that the short-time phase spectrum can significantly contribute to speech intelligibility over small window durations (i.e., 20–40 ms). This is an interesting result, indicating the possible usefulness of the short-time phase spectrum for ASR, which commonly employs small window durations of 20–40 ms for spectral analysis. In this paper, we continue our investigation of the short-time phase spectrum. We explore the use of partial short-time phase spectrum information, in the absence of all the short-time magnitude spectrum information, for intelligible signal reconstruction. We create two types of stimuli; one in which its frequency-derivative (i.e., group delay function, GDF) is preserved and another in which its time-derivative (i.e., instantaneous frequency distribution, IFD) is preserved. We do this to determine the contribution that each of these derivatives provides toward intelligibility. Reconstructing stimuli from knowledge of only the GDF or only the IFD results in poor intelligibility. However, when we create stimuli using knowledge of both the GDF and the IFD, reasonable intelligibility is obtained. In light of these results, we conclude that both the GDF and IFD components of the short-time phase spectrum are needed to reconstruct an intelligible signal. In addition, we also perform some experiments to quantify the intelligibility of stimuli reconstructed from the short-time phase and magnitude spectra of noisy speech. The intelligibility of stimuli constructed from either the short-time magnitude spectrum or the short-time phase spectrum degrades at a similar rate under increasing noise levels. The intelligibility of the original signals under noisy conditions also degrades with increased noise, but in all cases the intelligibility is superior to that provided by the stimuli constructed from the separate short-time components. Therefore, we argue that knowledge of both short-time magnitude and phase spectrum information results in superior human speech recognition performance.

Exponential-type distribution of human muscle sympathetic nerve activity results in an automatic quantification method

A new burst counting method based on a subject invariant characteristic demonstrates the limits of the actual automatic based methods. The exponential behaviour of the counted bursts in function of a variable threshold highlights a scaling property of the muscle sympathetic nerve activity. From experimental single unit recording results, we deduce the exponential-type (gamma) distribution of instantaneous spiking frequency within multi-unit recordings. We show that integrated muscle sympathetic nerve discharges must be gamma distributed with parameters proportional to the number of neurons in the recording pool and to the integration window width.