Related papers: High frequency limits in periodicity search from i…
The analysis of intermittent data is improved. The standard method of recovering the history of a particle cascade is proved in general not to reproduce the structure of the true cascade. The recovering corrections to the standard method…
A decentralized stability criterion is derived for a power system with heterogeneous subsystems. A condition for frequency stability and stability of interarea modes is derived using the generalized Nyquist criterion. The resulting scalable…
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
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 paper deals with the estimation of a sequence of frequencies from a corresponding sequence of signals. This problem arises in fields such as Doppler imaging where its specificity is twofold. First, only short noisy data records are…
Wideband analog signals push contemporary analog-to-digital conversion systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small…
Frequency estimation of multiple sinusoids is significant in both theory and application. In some application scenarios, only sub-Nyquist samples are available to estimate the frequencies. A conventional approach is to sample the signals at…
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…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
Searching for a weak signal at an unknown frequency is a canonical task in experiments probing fundamental physics such as gravitational-wave observatories and ultra-light dark matter haloscopes. These state-of-the-art sensors are limited…
This paper presents a significant modification to the Random Demodulator (RD) of Tropp et al. for sub-Nyquist sampling of frequency-sparse signals. The modification, termed constrained random demodulator, involves replacing the random…
A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…
In many applications of frequency estimation, the frequencies of the signals are so high that the data sampled at Nyquist rate are hard to acquire due to hardware limitation. In this paper, we propose a novel method based on subspace…
By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these…
New technological developments allow to explore the quantum properties of very complex systems, bringing the question of whether also macroscopic systems share such features, within experimental reach. The interest in this question is…
We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…