相关论文: Logical Signal Processing: a Fourier Analysis of T…

We extract the frequency content of a noisy signal by use of Discrete Fourier Transform. Our analysis overcomes the limitations imposed by incommensurate lattices. After computing the deterministic component, we show the relevance of the…

Rhythms and vibrations represent the quintessence of life, they are ubiquitous (systemic) in all living systems. Recognising, unfolding these rhythms is paramount in medicine, for example in the physiology of the heart, lung, hearing,…

The very old problem of extracting frequencies from time signals is addressed in the case of signals that are very short as compared to their intrinsic time scales. The solution of the problem is not only important to the classic signal…

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into…

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…

Spectrograms visualize the frequency components of a given signal which may be an audio signal or even a time-series signal. Audio signals have higher sampling rate and high variability of frequency with time. Spectrograms can capture such…

Metric Temporal Logic (MTL) is a popular formalism to specify temporal patterns with timing constraints over the behavior of cyber-physical systems with application areas ranging in property-based testing, robotics, optimization, and…

We present a robust control framework for time-critical systems in which satisfying real-time constraints robustly is of utmost importance for the safety of the system. Signal Temporal Logic (STL) provides a formal means to express a large…

We investigate the nature of the modifications in the temporal dynamics manifested in the high-frequency EEG spectra of the normal human brain in comparison to the diseased brain undergoing epilepsy. For this purpose, the Fourier…

Signal Temporal Logic monitoring over numerical simulation traces has emerged as an effective approach to approximate verification of continuous and hybrid systems. In this report we explore an exact verification procedure for STL…

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases.…

Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of…

In this paper, we provide a Dynamic Programming algorithm for on-line monitoring of the state robustness of Metric Temporal Logic specifications with past time operators. We compute the robustness of MTL with unbounded past and bounded…

E-science of photometric data requires automatic procedures and a precise recognition of periodic patterns to perform science as well as possible on large data. Analytical equations that enable us to set the best constraints to properly…

Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…

We propose an interval extension of Signal Temporal Logic (STL) called Interval Signal Temporal Logic (\ISTL). Given an STL formula, we consider an interval inclusion function for each of its predicates. Then, we use minimal inclusion…

The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with…

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…

New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…