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Due to its simultaneous deep imaging and integral field spectroscopic capability, an Imaging Fourier Transform Spectrograph (IFTS) is ideally suited to the Next Generation Space Telescope (NGST) mission, and offers opportunities for…
The Fast Fourier Transform (FFT) is a fundamental tool for signal analysis, widely used across various fields. However, traditional FFT methods encounter challenges in adjusting the frequency bin interval, which may impede accurate spectral…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
It is shown here that precision is gained by analyzing the interferometric spectra directly from the interferograms, with no previous Fourier transformation to put them in the standard frequency domain. The method is based on the…
The on-chip broadband optical spectrometers which cover the entire tissue transparency window ({\lambda}=650-1050 nm) with high resolution are highly demanded for the miniaturized bio-sensing and bio-imaging applications. Here, we propose a…
To reach the next frontier in multimode nonlinear optics, it is crucial to better understand the classical and quantum phenomena of systems with many interacting degrees of freedom -- both how they emerge and how they can be tailored to…
Slow motion movies are not only fascinating to watch, they also allow us to see intricate details of the mechanical dynamics of complex phenomena. If the images in each frame are replaced by terahertz (THz) waves, such movies can monitor…
Miniaturized spectrometers for Raman spectroscopy have the potential to open up a new chapter in sensing. Raman spectroscopy is essential for material characterization and biomedical diagnostics, however, its weak signal and the need for…
Harnessing the quantum interference of photon-pair generation processes, infrared quantum absorption spectroscopy (IRQAS) can extract the infrared optical properties of a sample through visible or near-infrared photon detection without the…
Due to its simultaneous deep imaging and integral field spectroscopic capability, an Imaging Fourier Transform Spectrograph (IFTS) is ideally suited to the Next Generation Space Telescope (NGST) mission, and offers opportunities for…
Synthesis of single-wavelength temporal phase-shifting algorithms (PSA) for interferometry is well-known and firmly based on the frequency transfer function (FTF) paradigm. Here we extend the single-wavelength FTF-theory to dual and…
Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…
Radio imaging is rapidly gaining prominence in the design of future communication systems, with the potential to utilize reconfigurable intelligent surfaces (RISs) as imaging apertures. Although the sparsity of targets in three-dimensional…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…
We present a rapid-scan, time-domain terahertz spectrometer employing femtosecond Er:fiber technology and an acousto-optic delay with attosecond precision, enabling scanning of terahertz transients over a 12.4 ps time window at a waveform…