Related papers: Effect of inter-sample spacing constraint on spect…
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency,…
Imaging devices exploit the Nyquist-Shannon sampling theorem to avoid both aliasing and redundant oversampling by design. Conversely, in medical image resampling, images are considered as continuous functions, are warped by a spatial…
Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating…
This paper introduces the class of ambiguity sparse processes, containing subsets of popular nonstationary time series such as locally stationary, cyclostationary and uniformly modulated processes. The class also contains aggregations of…
Spectroscopy sampling along delay time is typically performed with uniform delay spacing, which has to be low enough to satisfy the Nyquist-Shannon sampling theorem. The sampling theorem puts the lower bound for the sampling rate to ensure…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…
In this paper, aliasing effects are investigated for random fields defined on the d-dimensional sphere and reconstructed from discrete samples. First, we introduce the concept of an aliasing function on the sphere. The aliasing function…
One of the key approximations to range simulation is downscaling the image, dictated by the natural trigonometric relationships that arise due to long-distance viewing. It is well-known that standard downsampling applied to an image without…
In this paper we formalize, using the Nyquist-Shannon theorem, a fundamental temporal resolution limit for numerical experiments in complex systems. A consequence of this limit is aliasing, the introduction of spurious frequencies due to…
Sampling experiments provide a viable route to show quantum advantages of quantum devices over classical computers in well-defined computational tasks. However, quantum devices such as boson samplers are susceptible to various errors,…
This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different…
Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…
Context: Fourier transform (or lag) correlators in radio interferometers can serve as an efficient means of synthesising spectral channels. However aliasing corrupts the edge channels so they usually have to be excluded from the data set.…
In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not…