Cauchy Processes, Dissipative Benjamin–Ono Dynamics and Fat-Tail Decaying Solitons

In this paper, a dissipative version of the Benjamin–Ono dynamics is shown to faithfully model the collective evolution of swarms of scalar Cauchy stochastic agents obeying a follow-the-leaderinteraction rule. Due to the Hilbert transform, the swarm dynamic is described by nonlinear and non-local dynamics that can be solved exactly. From the mutual interactions emerges a fat-tail soliton that can be obtained in a closed analytic form. The soliton median evolves nonlinearly with time. This behaviour can be clearly understood from the interaction of mutual agents.

BPSK Modulation-Based Local Oscillator-Free IQ Demodulation for Millimeter Wave Imaging

The precision of local oscillator (LO) signal in in-phase and quadrature (IQ) demodulation strongly affects the imaging performance of millimeter wave (mmWave) radars. Therefore, to eliminate the requirement for high-precision LO, a simple yet effective digital IQ demodulation method has been proposed with the aid of a specified sampling scheme in order to eliminate the demand for LO. Based on the bandpass sampling theorem, the characteristic of the intermediate frequency signal of mmWave imaging indicates that the LO is unrequired if the sampling rate is twice of the frequency of the carrier of the intermediate signal. In this way, the in-phase signal would be directly and accurately obtained by performing the Binary-Phase-Shift-Keying (BPSK) modulation on the samples, based on which the IQ demodulation would be completed by using the Hilbert transform. The proposed method does not employ LO and thus simplifies the demodulation process and is suitable for implementation in a Field-Programmable Gate Array (FPGA) with fewer hardware resources. To verify the method, a three-dimensional mmWave radar imaging is carried out at the 30-34 GHz bandwidth, where the sampling and digital IQ demodulation are realized by an ADC (AD9250) and FPGA (XC7K325T), respectively. The results show a simplified transceiver with lower requirements and the prospect of the proposed method being applied in radar imaging and other related fields.

Acoustic emissions in the valuation of the combustion chamber pressure of an engine

Internal combustion engines demand advanced monitoring methodologies to promote efficient operation; particularly, the combustion pressure plays a central role in the overall performance, which promotes the utilization of transducers that hinders. Therefore, the present study introduces an acoustic emission methodology that serves for indirect combustion pressure measurements. Accordingly, the compound methodology integrates the Hilbert transform and the complex cepstrum using neural networks to accomplish pressure signal reconstruction. Results demonstrated that the proposed methodology featured robust performance while estimating pressure signals as it mitigates the combined noise effect produced by variations in engine speed, engine load, and fuel type. Moreover, the reconstructed signal facilitated the determination of key performance parameters such as peak pressure, pressure timing, and effective mean pressure. Relative error amounted to less than 10%, which ratified the robustness of the indirect pressure measurements. In conclusion, acoustic signal techniques represent an adequate approach to estimate the combustion pressure at variable engine conditions.

Lagged teleconnections of climate variables identified via complex rotated Maximum Covariance Analysis

A proper description of ocean-atmosphere interactions is key for a correct understanding of climate evolution. The interplay among the different variables acting over the climate is complex, often leading to correlations across long spatial distances (teleconnections). In some occasions, those teleconnections occur with quite significant temporal shifts that are fundamental for the understanding of the underlying phenomena but which are poorly captured by standard methods. Applying orthogonal decomposition such as Maximum Covariance Analysis (MCA) to geophysical data sets allows to extract common dominant patterns between two different variables, but generally suffers from (i) the non-physical orthogonal constraint as well as (ii) the consideration of simple correlations, whereby temporally offset signals are not detected. Here we propose an extension, complex rotated MCA, to address both limitations. We transform our signals using the Hilbert transform and perform the orthogonal decomposition in complex space, allowing us to correctly correlate out-of-phase signals. Subsequent Varimax rotation removes the orthogonal constraints, leading to more physically meaningful modes of geophysical variability. As an example of application, we have employed this method on sea surface temperature and continental precipitation; our method successfully captures the temporal and spatial interactions between these two variables, namely for (i) the seasonal cycle, (ii) canonical ENSO, (iii) the global warming trend, (iv) the Pacific Decadal Oscillation, (v) ENSO Modoki and finally (vi) the Atlantic Meridional Mode. The complex rotated modes of MCA provide information on the regional amplitude, and under certain conditions, the regional time lag between changes on ocean temperature and land precipitation.

Response to “Limitations in the Hilbert Transform Approach to Locating Solar Cycle Terminators” by R. Booth

Booth (Solar Phys.296, 108, 2021; hereafter B21) is essentially a critique of the Hilbert transform techniques used in our paper (Leamon et al., Solar Phys.295, 36, 2020; hereafter L20) to predict the termination of solar cycles. Here we respond to his arguments; our methodology and parameter choices do extract a mathematically robust signature of terminators from the historical sunspot record. We agree that the attempt in L20 to extrapolate beyond the sunspot record gives a failed prediction for the next terminator of May 2020, and we identify both a possible cause and remedy here. However, we disagree with the B21 assessment that the likely termination of Solar Cycle 24 is two years after the date predicted in L20, and we show why.

Time-Frequency Processing

The idea of dynamic spectral processing, introduced at the end of the previous chapter is fully developed here. The principle of sub-band analysis and synthesis is shown as the basis for a time-varying frequency-domain approach. The short-time Fourier transform (STFT) is introduced as a sequence of time-ordered DFT frames from which amplitude and phase data can be obtained. Different methods for instantaneous frequency estimation are discussed. A streaming system for dynamic spectral processing is introduced, and various modification techniques are explored. The latter part of the chapter presents the Hilbert transform as yet another streaming spectral processing application. The chapter concludes with further additions to the notions of spectrum developed earlier in the volume.

Real-time estimation of phase and amplitude with application to neural data

Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal’s past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient’s beta-band brain activity.

Modeling tilt noise caused by atmospheric processes at long periods for several horizontal seismometers at BFO - a reprise

Summary Tilting of the ground due to loading by the variable atmosphere is known to corrupt very long-period horizontal seismic records (below 10 mHz) even at the quietest stations. At BFO (Black Forest Observatory, SW-Germany) the opportunity arose to study these disturbances on a variety of simultaneously operated state-of-the-art broadband sensors. A series of time windows with clear atmospherically caused effects was selected and attempts were made to model these “signals” in a deterministic way. This was done by simultaneously least squares fitting the locally recorded barometric pressure and its Hilbert transform to the ground accelerations in a bandpass between 100 and 3600 s periods. Variance reductions of up to 97 per cent were obtained. We show our results by combining the “specific pressure induced accelerations” for the two horizontal components of the same sensor as vectors on a horizontal plane, one for direct pressure and one for its Hilbert transform. It turned out that at BFO the direct pressure effects are large, strongly position dependent, and largely independent of atmospheric events for instruments installed on piers, while three posthole sensors are only slightly affected. The infamous “cavity effects” are invoked to be responsible for these large effects on the pier sensors. On the other hand, in the majority of cases all sensors showed very similar magnitudes and directions for the vectors obtained for the regression with the Hilbert transform, but highly variable from event to event especially in direction. Therefore this direction most certainly has to do with the gradient of the pressure field moving over the station which causes a larger scale deformation of the crust. The observations are very consistent with these two fundamental mechanisms of how fluctuations of atmospheric surface pressure causes tilt noise. The results provide a sound basis for further improvements of the models for these mechanisms. The methods used here can already help to reduce atmospherically induced noise in long period horizontal seismic records .