The Truncated Fourier Transform (tft) is a variation of the Discrete Fourier Transform (dft/fft) that allows for input vectors that do not have length 2 n for n a positive integer. We present the univariate version of the tft, originally due to Joris van der Hoeven, heavily illustrating the presentation in order to make these methods accessible to a broader audience.

We test various features for recognition of leaves of wooden species. We compare Fourier descriptors, Zernike moments, Legendre moments and Chebyshev moments. All the features are computed from the leaf boundary only. Experimental evaluation on real data indicates that Fourier descriptors slightly outperform the other tested features.

background and aims. polymerization efficacy affects the properties and performance of composite resin restorations. the purpose of this study was to evaluate the effectiveness of polymerization of two micro-hybrid, two nano-hybrid and one nano-filled ormocer-based composite resins, cured by two different light-curing systems, using fourier transformation infrared (ft-ir) spectroscopy and vicke...

in this paper, we propose a new residual analysis method using fourier series transform into fuzzy time series model for improving the forecasting performance. this hybrid model takes advantage of the high predictable power of fuzzy time series model and fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...

Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast (NUFFT) an alternative approach that has been mostly overlooked. With aid of experiments on a high-resolution interferometer with variety optical sources, these two methods are compared. It found NUFFT comparable in spectral profile sha...

The frequency-domain finite-difference (FD-FD) methods have been successfully used to obtain numerical solutions of the twodimensional (2-D) Helmholtz equation. The standard second-order accurate FD-FD scheme is known to produce unwanted numerical spatial and temporal dispersions when the sampling is inadequate. Recently compact higher-order accurate FD-FD methods have been proposed to reduce t...

A partial Butson matrix is a matrix H ∈ MM×N (Zq) having its rows pairwise orthogonal, where Zq ⊂ C× is the group of q-th roots of unity. We investigate here the counting problem for these matrices in the “thin” regime, where M = 2, 3, . . . is small, and where N → ∞ (subject to the condition N ∈ pN when q = pk > 2). The proofs are inspired from the de Launey-Levin and Richmond-Shallit counting...

We give a detailed study of the discrete Fourier transform (DFT) of r-even arithmetic functions, which form a subspace of the space of r-periodic arithmetic functions. We consider the DFT of sequences of r-even functions, their mean values and Dirichlet series. Our results generalize properties of the Ramanujan sum. We show that some known properties of r-even functions and of the Ramanujan sum...