Raman spectral data collected with high-resolution laboratory spectrometers are processed into a format suitable for importing as a user library on a 1064 nm DeltaNu first generation, field-deployable spectrometer prototype. The two laboratory systems used are a 1064 nm Bruker Fourier transform (FT)-Raman spectrometer and a 785 nm Kaiser dispersive spectrometer. The steps taken to adapt for dev...

In this work, we present the analytic treatment of the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar including spin down corrections in a parametrized model discussed by Brady et. al. [1]. The formalism lends itself to a development of the FT in terms of well known special functions and integrals defining the spin down moments.

In this work we synthesized of mesoporous silica nanoparticles and functionalized with 3-aminopropyltriethoxysilane to improve the loading and release of ibuprofen bonded to 3-aminopropyltriethoxysilane. sample were characterized by Fourier transform infrared spectroscopy, Scanning electron microscopy , X-ray diffraction, and ultraviolet-visible. the Fourier transform infrared spectroscopy resu...

A novel and automated technique is described for removing fMRI image artifacts resulting from motion outside of the imaging field of view. The technique is based on the Stockwell transform (ST), a mathematical operation that provides the frequency content at each time point within a time-varying signal. Using this technique, 1D Fourier transforms (FTs) are performed on raw image data to obtain ...

The methods of fast parallel calculation of multidimensional hypercomplex discrete Fourier transform (HDFT) are discussed. The theoretical and experimental estimation of parallelization efficiency is given. It is shown that proposed method has very high efficiency (up to 90%).

In this paper we introduce convolution theorem for the Fourier transform (FT) of two complex functions. We show that the correlation theorem for the FT can be derived using properties of convolution. We develop this idea to derive the correlation theorem for the quaternion Fourier transform (QFT) of the two quaternion functions.

We analyze the minimum achievable mean-square error in frequency-modulated continuous-wave range estimation of a single stationary target when photon-counting detectors are employed. Starting from the probability density function for the photon-arrival times in photodetectors with subunity quantum efficiency, dark counts, and dead time, we derive the Cramér-Rao bound and highlight three importa...

An analytical and concise formula is derived for the fractional Fourier transform (FRT) of partially coherent beams that is based on the tensorial propagation formula of the cross-spectral density of partially coherent twisted anisotropic Gaussian-Schell-model (GSM) beams. The corresponding tensor ABCD law performing the FRT is obtained. The connections between the FRT formula and the generaliz...

In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as add...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...