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The ability to sense propagating electromagnetic plane waves based on their directions of arrival (DOAs) is fundamental to a range of radio frequency (RF) sensing, communications, and imaging applications. This paper introduces an algorithm for the wideband true time delay digital delay Vandermonde matrix (DVM), utilizing Thiran fractional delays that are useful for realizing RF sensors having multiple look DOA support. The digital DVM algorithm leverages sparse matrix factorization to yield multiple simultaneous RF beams for low-complexity sensing applications. Consequently, the proposed algorithm offers a reduction in circuit complexity for multi-beam digital wideband beamforming systems employing Thiran fractional delays. Unlike finite impulse response filter-based approaches which are wideband but of a high filter order, the Thiran filters trade usable bandwidth in favor of low-complexity circuits. The phase and group delay responses of Thiran filters with delays of a fractional sampling period will be demonstrated. Thiran filters show favorable results for sample delay blocks with a temporal oversampling factor of three. Thiran fractional delays of orders three and four are mapped to Xilinx FPGA RF-SoC technologies for evaluation. The preliminary results of the APF-based Thiran fractional delays on FPGA can potentially be used to realize DVM factorizations using application-specific integrated circuit (ASIC) technology. [ABSTRACT FROM AUTHOR]

The Laplace transform is a central mathematical tool for analysing 1D/2D signals and for the solution to PDEs; however, its definition and computation on arbitrary data is still an open research problem. We introduce the Laplace transform on arbitrary domains and focus on the spectral Laplace transform, which is defined by applying a 1D filter to the Laplacian spectrum of the input domain. The spectral Laplace transform satisfies standard properties of the 1D and 2D transforms, such as dilation, translation, scaling, derivation, localisation, and relations with the Fourier transform. The spectral Laplace transform is enough general to be applied to signals defined on different discrete data, such as graphs, 3D surface meshes, and point sets. Working in the spectral domain and applying polynomial and rational polynomial approximations, we achieve a stable computation of the spectral Laplace Transform. As main applications, we discuss the computation of the spectral Laplace Transform of functions defined on arbitrary domains (e.g., 2D and 3D surfaces, graphs), the solution of the heat diffusion equation, and graph signal processing. [ABSTRACT FROM AUTHOR]

Infrared (IR) spectrometers, particularly the aging ones, often suffer from the band overlap and random noise. In this paper, a blind estimation method based on discrete cosine transform (DCT) regularization is proposed for IR spectrum measured from an aging spectrometer instrument. Motivated by the observation that the DCT coefficient distribution of the ground-truth spectrum is sparser than that of the observed spectrum, an IR spectral deconvolution model is formulated in our method to regularize the distribution of the observed spectrum by total variation regularization. Then, the split Bregman method is exploited to solve the resulting optimization problem. The experimental results demonstrate an encouraging performance of the proposed approach to suppress noise and preserve spectral details. The novelty of our method lies on its ability to estimate instrument function and latent spectrum in a joint framework; thus, mitigating the effects of instrument aging to a large extent. The recovered IR spectra can efficiently capture the spectral features and interpret the unknown chemical mixture in industrial applications. [ABSTRACT FROM AUTHOR]

This paper proposes a new system for the unsupervised diagnostic and monitoring of defects in waveguide imaging. The proposed method is automatic and does not require manual selection of specific frequencies for defect diagnostics. The core of the method is a computational intelligent machine learning algorithm based on sparse non-negative matrix factorization. An internal functionality is built into the machine learning algorithm to adaptively learn and control the sparsity of the factorization, and to render better accuracy in detecting defects. This is achieved by using Bayesian statistics methodology. The proposed method is demonstrated on automatic detection of defect in metals. In addition, we show that the extraction of the spectrum signature corresponding to the defect is significantly more efficient with the proposed optimal sparsity, which subsequently led to better detection performance. Experimental tests and comparisons with other sparse factorization methods have been conducted to verify the efficacy of the proposed method. [ABSTRACT FROM PUBLISHER]

We propose a novel method for measuring the pitch of a speech signal based on the calculation and subsequent processing of the autocorrelation function of the signal, emphasizing its peak associated with the signal's period. The proposed processing prevents gross errors in pitch measurement and represents a type of clipping of the positive peaks in the autocorrelation function. [ABSTRACT FROM AUTHOR]

Nowadays, the impact of the ships on the World economy is enormous, considering that every ship needs fuel to sail from source to destination. It requires a lot of fuel, and therefore, there is a need to monitor and predict a ship's average fuel consumption. However, although there are much models available to predict a ship's consumption, most of them rely on a uniform time set. Here we show the model of predicting external influences to ship's average fuel consumption based on a non-uniform time set. The model is based on the numeric fitting of recorded data. The first set of recorded data was used to develop the model, while the second set was used for validation. Statistical quality measures have been used to choose the optimal fitting function for the model. According to statistical measures, the Gaussian 7, Fourier 8, and smoothing spline fitting functions were chosen as optimal algorithms for model development. In addition to extensive data analysis, there is an algorithm for filter length determination for the preprocessing of raw data. This research is of interest to corporate logistics departments in charge of ensuring adequate fuel for fleets when and where required. [ABSTRACT FROM AUTHOR]