Generation of cyclically permutable codes by galois field Fourier transform

2016 ◽  
Author(s):  
Ting-Ya Yang ◽  
Houshou Chen ◽  
Kuo-Cheng Chung
Keyword(s):  
Fourier Transform ◽  
Galois Field

Multiplier-Free Implementation of Galois Field Fourier Transform on a FPGA

2019 ◽  
Vol 66 (11) ◽  
pp. 1815-1819
Author(s):  
Sree Balaji Girisankar ◽  
Mona Nasseri ◽  
Jennifer Priscilla ◽  
Shu Lin ◽  
Venkatesh Akella
Keyword(s):  
Fourier Transform ◽  
Galois Field

scholarly journals New application of non-binary Galois fields Fourier transform: digital analog of convolution theorem

2021 ◽  
Vol 23 (3) ◽  
pp. 1718
Author(s):  
Elizaveta S. Vitulyova ◽  
Dinara K. Matrassulova ◽  
Ibragim E. Suleimenov
Keyword(s):  
Neural Networks ◽  
Fourier Transform ◽  
Linear Systems ◽  
Galois Field ◽  
Convolution Theorem ◽  
Time Shift ◽  
Digital Signals ◽  
Galois Fields ◽  
Analog Signals ◽  
Signal Processing Methods

It is shown that the use of the representation of digital signals varying in the restricted amplitude range through elements of Galois fields and the Galois field Fourier transform makes it possible to obtain an analogue of the convolution theorem. It is shown that the theorem makes it possible to analyze digital linear systems in same way that is used to analyze linear systems described by functions that take real or complex values (analog signals). In particular, it is possibile to construct a digital analogue of the transfer function for any linear system that has the property of invariance with respect to the time shift. It is shown that the result obtained has a fairly wide application, in particular, it is of interest for systems in which signal processing methods are combined with the use of neural networks.

scholarly journals Some advantages of non-binary Galois fields for digital signal processing

2021 ◽  
Vol 23 (2) ◽  
pp. 871
Author(s):  
Inabat Moldakhan ◽  
Dinara K. Matrassulova ◽  
Dina B. Shaltykova ◽  
Ibragim E. Suleimenov
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Digital Signal ◽  
Galois Field ◽  
Prime Numbers ◽  
Sampling Interval ◽  
Signal Spectrum ◽  
Galois Fields ◽  
Digital Spectrum ◽  
The Fourier Transform

It is shown that the convenient processing facilities of digital signals that varying in a finite range of amplitudes are non-binary Galois fields, the numbers of which elements are equal to prime numbers. Within choosing a sampling interval which corresponding to such a Galois field, it becomes possible to construct a Galois field Fourier transform, a distinctive feature of which is the exact correspondence with the ranges of variation of the amplitudes of the original signal and its digital spectrum. This favorably distinguishes the Galois Field Fourier Transform of the proposed type from the spectra, which calculated using, for example, the Walsh basis. It is also shown, that Galois Field Fourier Transforms of the proposed type have the same properties as the Fourier transform associated with the expansion in terms of the basis of harmonic functions. In particular, an analogue of the classical correlation, which connected the signal spectrum and its derivative, was obtained. On this basis proved, that the using of the proposed type of Galois fields makes it possible to develop a complete analogue of the transfer function apparatus, but only for signals presented in digital form.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

FR-IR Molecular Microanalysis System

1990 ◽  
Vol 48 (2) ◽  
pp. 270-271
Author(s):  
John A. Reffner ◽  
William T. Wihlborg
Keyword(s):  
Fourier Transform ◽  
Fourier Transform Infrared ◽  
Integrated System ◽  
Morphological Examination ◽  
Fully Integrated ◽  
Ir Microscopy ◽  
Normal Functions ◽  
Infrared Microspectroscopy ◽  
Infrared Spectral ◽  
Ft Ir

The IRμs™ is the first fully integrated system for Fourier transform infrared (FT-IR) microscopy. FT-IR microscopy combines light microscopy for morphological examination with infrared spectroscopy for chemical identification of microscopic samples or domains. Because the IRμs system is a new tool for molecular microanalysis, its optical, mechanical and system design are described to illustrate the state of development of molecular microanalysis. Applications of infrared microspectroscopy are reviewed by Messerschmidt and Harthcock.Infrared spectral analysis of microscopic samples is not a new idea, it dates back to 1949, with the first commercial instrument being offered by Perkin-Elmer Co. Inc. in 1953. These early efforts showed promise but failed the test of practically. It was not until the advances in computer science were applied did infrared microspectroscopy emerge as a useful technique. Microscopes designed as accessories for Fourier transform infrared spectrometers have been commercially available since 1983. These accessory microscopes provide the best means for analytical spectroscopists to analyze microscopic samples, while not interfering with the FT-IR spectrometer’s normal functions.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

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