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Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 THz region, and in other bands enables metrological comparison between…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
Spectral envelope is one of the most important features that characterize the timbre of an instrument sound. However, it is difficult to use spectral information in the framework of conventional spectrogram decomposition methods. We…
We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…
This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…
Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the…
Label free tracking of small bio-particles such as proteins or viruses is of great utility in the study of biological processes, however such experiments are frequently hindered by weak signal strengths and a susceptibility to scattering…
Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also…
In this Chapter we review the challenges of, and opportunities for, 3D spectroscopy, and how these have lead to new and different approaches to sampling astronomical information. We describe and categorize existing instruments on 4m and 10m…
High-precision optical frequency measurement is indispensable to modern science and technology, yet conventional spectroscopic techniques struggle to resolve sub-linewidth spectral features. We introduce a unique platform for…
Hyperspectral images are high-dimensional datasets comprising hundreds of contiguous spectral bands, enabling detailed analysis of materials and surfaces. Hyperspectral anomaly detection (HAD) refers to the technique of identifying and…
Recent advances in techniques for generating quantum light have stimulated research on novel spectroscopic measurements using quantum entangled photons. One such spectroscopy technique utilizes non-classical correlations among entangled…
Spectrum sensing is of critical importance in any cognitive radio system. When the primary user's signal has uncertain parameters, the likelihood ratio test, which is the theoretically optimal detector, generally has no closed-form…
Spatial resolution of most imaging devices is fundamentally restricted by diffraction. This limitation is manifested in the loss of high spatial frequency information contained in evanescent waves. As a result, conventional far-field optics…
The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
Holography has always held special appeal, for it is able to record and display spatial information in three dimensions. Here, we show how to augment the capabilities of digital holography by using a large number of narrow laser lines at…