Related papers: Low frequency fringe pattern analysis via a Fourie…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
This paper consists of two parts. First, the (undirected) Hamiltonian path problem is reduced to a signal filtering problem - number of Hamiltonian paths becomes amplitude at zero frequency for (a combination of) sinusoidal signal f(t) that…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…
Fourier transform spectroscopy (FTS) has been widely used as an analytical tool for many applications in science and engineering. In this paper, we describe the operation principle and practical implementation of an FTS prototype. First,…
Fourier Ptychography is a recently proposed imaging technique that yields high-resolution images by computationally transcending the diffraction blur of an optical system. At the crux of this method is the phase retrieval algorithm, which…
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…
Conventional dual-frequency fringe projection algorithm often suffers from phase unwrapping failure when the frequency ratio between the high frequency and the low one is too large. Zhang et.al. proposed an enhanced two-frequency…
Accurate phase extraction from sinusoidal signals is a crucial task in various signal processing applications. While prior research predominantly addresses the case of asynchronous sampling with unknown signal frequency, this study focuses…
In this paper we deal with the linear frequency modulated signals and radar signals that are affected by disturbance which is the inevitable phenomenon in everyday communications. The considered cases represent the cases when the signals of…
The extraction of information carried by light plays an increasingly important role in optical communication, imaging, and detection. However, the information can only be successfully extracted when the light pulse is comparably strong,…
Resonance frequencies can provide useful information on the deformation occurring during fracturing experiments or $CO_2$ management, complementary to the microseismic event distribution. An accurate time-frequency representation is of…
Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier…
Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the…
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…
In this paper, we describe the principle of a multi-aperture interferometer that uses a phase-shifting technique and is suitable for quick, snapshot imaging of astrophysical objects at extreme angular resolution through Fourier inversion. A…
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
This study introduces a short-time Fourier transform-based method for reconstructing signals encoded using modulo analog-to-digital converters with 1-bit folding information. In contrast to existing Fourier-based reconstruction approaches…
Retrieving object phase from the optical fringe pattern is a critical task in quantitative phase imaging and often requires appropriate image preprocessing (background and noise minimization), especially when retrieving phase from the…
Fringe field becomes important when one requires more accurate modeling of a ring lattice to study the long-term beam dynamics in storage rings and deal with large aperture magnets in high-intensity proton synchrotrons or accumulator rings.…
The basic principle of astronomical interferometry is to derive the angular distribution of radiation in the sky from the Fourier transform of the electric field on the ground. What is so special about the Fourier transform? Nothing, it…