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Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Discrete Fractional Fourier Transforms (DFrFT) are universal mathematical tools in signal processing, communications and microwave sensing. Despite the excessive applications of DFrFT, implementation of corresponding fractional orders in…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
In this work we numerically analyze a passive photonic integrated neuromorphic accelerator based on hardware-friendly optical spectrum slicing nodes. The proposed scheme can act as a fully analogue convolutional layer, preprocessing…
Intrinsic spectrum that results from the coupling of spontaneous emission in a laser cavity, can determine the energy concentration and coherence of lasers, which is crucial for the optical high-precision measurement. Up to now, it is hard…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide…
With recent rapid advances in photonic integrated circuits, it has been demonstrated that programmable photonic chips can be used to implement artificial neural networks. Convolutional neural networks (CNN) are a class of deep learning…
To comprehensively assess optical fiber communication system conditions, it is essential to implement joint estimation of the following four critical impairments: nonlinear signal-to-noise ratio (SNRNL), optical signal-to-noise ratio…
Source wavelet estimation is the key in seismic signal processing for resolving subsurface structural properties. Homomorphic deconvolution using cepstrum analysis has been an effective method for wavelet estimation for decades. In general,…
In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…
Visible-infrared object detection has gained sufficient attention due to its detection performance in low light, fog, and rain conditions. However, visible and infrared modalities captured by different sensors exist the information…
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…
This paper demonstrates the operation of a universal RF photonic circuit that consists of a generalized Mach Zehnder Interferometer architecture with its Nx1 combiner replaced by a NxN optical DFT network. The proposed circuit architecture…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…