Related papers: The Discrete Hilbert Transform for Non-Periodic Si…
This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be…
The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in…
The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior…
This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being…
Dispersionless bands -- flatbands -- have been actively studied thanks to their interesting properties and sensitivity to perturbations, which makes them natural candidates for exotic states. In parallel non-Hermitian systems have attracted…
The Hilbert transform has been one of the foundational transforms in signal processing, finding it's way into multiple disciplines from cryptography to biomedical sciences. However, there does not exist any quantum analogue for the Hilbert…
The capability to temporarily arrest the propagation of optical signals is one of the main challenges hampering the ever more widespread use of light in rapid long-distance transmission as well as all-optical on-chip signal processing or…
The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency…
In recent years, multiple sensor-based devices and systems have been deployed in smart agriculture, industrial automation, E-Health, etc. The diversity of sensor data types and the amount of data pose critical challenges for data…
Nonlinear metasurfaces that dynamically manipulate the phase of a passing light beam are of interest for a wide range of applications. The controlled operation of such devices requires accurate measurements of the optical transmission phase…
Harmonic analysis has provided powerful tools to accurately determine the tune from turn-by-turn data originating from numerical simulations or beam measurements in circular accelerators and storage rings. Methods that have been developed…
A many to one discrete auditory transform is presented to map a sound signal to a perceptually meaningful spectrum on the scale of human auditory filter band widths (critical bands). A generalized inverse is constructed in closed analytical…
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution…
Recent results on source-channel coding for secure transmission show that separation holds in several cases under some less-noisy conditions. However, it has also been proved through a simple counterexample that pure analog schemes can be…
We demonstrate the emergence of an entire flat band embedded in dispersive bands at the exceptional point of a PT symmetric photonic lattice. For this to occur, the gain and loss parameter effectively alters the size of the partial flat…
In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on…
Secure distributed data compression in the presence of an eavesdropper is explored. Two correlated sources that need to be reliably transmitted to a legitimate receiver are available at separate encoders. Noise-free, limited rate links from…
This paper presents 10-point and 12-point versions of the recently introduced number theoretic Hilbert (NHT) transforms. Such transforms have applications in signal processing and scrambling. Polymorphic solutions with respect to different…
The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…
We propose occupying guard-bands in closely-spaced WDM systems with redundant signal spectral components, to increase tolerance to frequency misalignment and channel shaping from multiplexing elements. By cyclically repeating the spectrum…