Related papers: On the Concept of Frequency in Signal Processing
Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image…
In this paper, we argue that some fundamental concepts and tools of signal processing may be effectively applied to represent and interpret social cognition processes. From this viewpoint, individuals or, more generally, social stimuli are…
A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…
This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and…
A finite-energy signal is represented by a square-integrable, complex-valued function $t\mapsto s(t)$ of a real variable $t$, interpreted as time. Similarly, a noisy signal is represented by a random process. Time-frequency analysis, a…
The fundamental frequency is one of the parameters that define power quality. Correctly determining this parameter under the conditions that prevail in modern power grids is crucial. Diagnostic purposes often require an efficient estimation…
Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
In this work, we consider the modeling of signals that are almost, but not quite, harmonic, i.e., composed of sinusoids whose frequencies are close to being integer multiples of a common frequency. Typically, in applications, such signals…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
Frequency analysis is useful for understanding the mechanisms of representation learning in neural networks (NNs). Most research in this area focuses on the learning dynamics of NNs for regression tasks, while little for classification.…
Optical spectroscopy is an important and widely used technique, for instance, to characterize new materials and to identify unknown compounds. Spectra are typically reported as a function of the wavelength of light, yet the information…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
Coherence is a basic phenomenon in quantum mechanics and considered to be an essential resource in quantum information processing. Although the quantification of coherence has attracted a lot of interest, the lack of efficient methods to…
Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology…
To excel in signal processing or control systems, a deep understanding of transforms is essential. But what exactly is this mathematical tool, and how does it function? In this article, we will explore the fundamentals of transforms, their…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…