相关论文: On the Concept of Frequency in Signal Processing
The complexity of a system description is a function of the entropy of its symbolic description. Prior to computing the entropy of the system description, an observation scale has to be assumed. In natural language texts, typical scales are…
Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses \textit{in silico} and predict the outcome of experiments and interactions that are very hard…
Signal analysis is built upon various resolutions of the identity in signal vector spaces, e.g. Fourier, Gabor, wavelets, etc. Similar resolutions are used as quantizers of functions or distributions, paving the way to a time-frequency or…
The generation of time signals is a fundamental task in science. Here we study the relation between the quality of a time signal and the physics of the system that generates it. According to quantum theory, any time signal can be decomposed…
Frequency discrimination is a fundamental task of the auditory system. The mammalian inner ear, or cochlea, provides a place code in which different frequencies are detected at different spatial locations. However, a temporal code based on…
The frequency response function (FRF) is an established way to describe the outcome of experiments in posture control literature. The FRF is an empirical transfer function between an input stimulus and the induced body segment sway profile,…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
The monitoring of event frequencies can be used to recognize behavioral anomalies, to identify trends, and to deduce or discard hypotheses about the underlying system. For example, the performance of a web server may be monitored based on…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Experimental exploration of synchronization in scalable oscillator micro systems has unfolded a deeper understanding of networks, collective phenomena, and signal processing. Cavity optomechanical devices have played an important role in…
This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…
Learning models or control policies from data has become a powerful tool to improve the performance of uncertain systems. While a strong focus has been placed on increasing the amount and quality of data to improve performance, data can…
Curiously overlooked in physics is its dependence on the transmission of numbers. For example the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical…
Despite their ability to represent highly expressive functions, deep learning models seem to find simple solutions that generalize surprisingly well. Spectral bias -- the tendency of neural networks to prioritize learning low frequency…
We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…
Time-frequency representations are important for the analysis of time series. We have developed an online time-series analysis system and equipped it to reliably handle re-alignment in the time-frequency plane. The system can deal with…
Mathematical Theory of Evidence (MTE) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain…
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…
Certain quantum sensing protocols rely on qubits that are initialized, coherently driven in the presence of a stimulus to be measured, then read out. Most widely employed pulse sequences used to drive sensing qubits act locally in either…
A modulated oscillation in two or three dimensions can be represented as the trajectory traced out in space by a particle orbiting an ellipse, the properties of which vary as a function of time. Generalizing ideas from signal analysis, the…