High-Precision and High-Resolution Synchrosqueezing Transform via Time-Frequency Instantaneous Phases

Synchrosqueezing transform (SST) can effectively improve time-frequency precision and resolution by squeezing time-frequency spectra via instantaneous frequencies, and it has been applied in many diverse disciplines; however, the precision of estimated instantaneous frequencies during SST is usually affected by the time-sample interval of the inputted signal; this usually leads to low-precision or inaccurate SST results and limits its further application. To obtain high-precision and high-resolution SST results with high efficiency, we propose a high-precision and high-resolution SST via time-frequency instantaneous phases (HSST); in HSST, time-frequency instantaneous phases with period-jumps removal are used for high-precision instantaneous frequencies estimation and SST. Two synthetic signal examples show that HSST can minimize the impact of the time-sample interval to achieve high-precision and high-resolution SST results with high efficiency. A real 3D seismic data application demonstrates that HSST has fantastic performance in time-frequency precision and resolution enhancement, and it can be widely used in digital signals processing and interpretation fields.

Green notes: The rhythms of cyanobacteria exoelectrogenesis as de-composed by the Hilbert-Huang transform

Electrons from cyanobacteria photosynthetic and respiratory systems are implicated in current generated in biophotovoltaic (BPV) devices. However, the pathway that electrons follow to electrodes remains largely unknown, limiting progress of applied research. Here we use Hilbert-Huang transforms to decompose Synechococcus elongatus sp. PCC7942 BPV current density profiles into physically meaningful oscillatory components, and compute their instantaneous frequencies. We develop hypotheses for the genesis of the oscillations via repeat experiments with iron-depleted and 20% CO2 enriched biofilms. The oscillations exhibit rhythms that are consistent with the state of the art cyanobacteria circadian model, and putative exoelectrogenic pathways. In particular, we observe oscillations consistent with: rhythmic D1:1 (photosystem II core) expression; circadian-controlled glycogen accumulation; circadian phase shifts under modified intracellular %ATP; and circadian period shortening in the absence of the iron-sulphur protein LdpA. We suggest that the extracted oscillations may be used to reverse-identify proteins and/or metabolites responsible for cyanobacteria exoelectrogenesis.

Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

Adaptive complementary ensemble EMD and energy-frequency spectra of cryptocurrency prices

In this study, we study the price dynamics of cryptocurrencies using adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis. This is a multiscale noise-assisted approach that decomposes any time series into a number of intrinsic mode functions, along with the corresponding instantaneous amplitudes and instantaneous frequencies. The decomposition is adaptive to the time-varying volatility of each cryptocurrency price evolution. Different combinations of modes allow us to reconstruct the time series using components of different timescales. We then apply Hilbert spectral analysis to define and compute the instantaneous energy-frequency spectrum of each cryptocurrency to illustrate the properties of various timescales embedded in the original time series.

Analytical Analysis of Interaction Between a Heavy Vehicle and a Simply Supported Light Bridge Based on Frequency Modulation

This paper analyzes the interaction between a heavy vehicle and a simply supported light bridge based on frequency modulation technique, in which variations of instantaneous frequencies of both bridge and heavy vehicle are considered. The bridge is modeled as a simply supported Euler beam and the heavy vehicle is simplified as a spring-mass system. The variation of instantaneous frequencies of both bridge and vehicle induced by the moving vehicle is usually neglected in classical analysis to decouple the pair of governing equations. However, the coupled vehicle–bridge interaction (VBI) system becomes time-varying and the pair of governing equations cannot be decoupled when the vehicle/bridge mass ratio cannot be neglected. The instantaneous frequencies of both bridge and heavy vehicle including their higher vibration modes are investigated herein. An analytical solution describing the dynamic response of the time-varying VBI system is developed by using the frequency modulation technique. Both Finite Element (FE) method and published experimental data are used for comparison purpose. The predictions of the proposed method match better with those obtained from the FE simulations and experimental measurements than the classical method. Five numerical examples have been adopted to compare the performance of the proposed model and the classical method: the former performs generally well, especially when the vehicle is heavy, or the vehicle frequency is near to the bridge frequency. The classical method is only a special case of the proposed model if either the mass or the stiffness of the vehicle is relatively small compared to the corresponding terms of the bridge. The performance of the proposed method has also been examined in four typical scenarios, where vehicle damping, multi-degree-of-freedom (MDOF) vehicle, road surface roughness, and two-span continuous bridge are involved.

Short-Time Fourier Transform Using Odd Symmetric Window Function

In this paper, a novel time-frequency (TF) analysis method, called the short-time Fourier transform using odd symmetric window function (OSTFT), is proposed by using odd symmetric window function to replace the conventional even window function of STFT. Different from conventional STFT acquiring the amplitude maximum at time and frequency centers, OSTFT acquires the minimum amplitude of 0. Hence, OSTFT can obtain a TFR with high TF resolution by utilizing the leaked energy rather than restraining it. It is worth to mention that the proposed OSTFT can vitiate the effect of window size we choose on the TFR obtained. Furthermore, it also has a good performance on signals with complex instantaneous frequencies (IF), even crossing IFs. Because we just replace the conventional window function of STFT, the time-consuming of the proposed OSTFT is at the same level as the conventional STFT. The effectiveness of proposed OSTFT has been validated on two complex multi-component simulated numerical signals and a signal collected from the brown bat.