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.

scholarly journals Deep Unsupervised 4-D Seismic 3-D Time-Shift Estimation With Convolutional Neural Networks

2021 ◽  
pp. 1-16
Author(s):  
Jesper Soren Dramsch ◽  
Anders Nymark Christensen ◽  
Colin MacBeth ◽  
Mikael Luthje
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Time Shift

scholarly journals Optical Axons for Electro-Optical Neural Networks

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6119
Author(s):  
Mircea Hulea ◽  
Zabih Ghassemlooy ◽  
Sujan Rajbhandari ◽  
Othman Isam Younus ◽  
Alexandru Barleanu
Keyword(s):  
Neural Networks ◽  
Optical Signal ◽  
Sensor Data ◽  
Line Of Sight ◽  
Optical Intensity ◽  
Digital Signals ◽  
Link Length ◽  
Optical Neural Networks ◽  
Analogue Signals ◽  
Neural Unit

Recently, neuromorphic sensors, which convert analogue signals to spiking frequencies, have been reported for neurorobotics. In bio-inspired systems these sensors are connected to the main neural unit to perform post-processing of the sensor data. The performance of spiking neural networks has been improved using optical synapses, which offer parallel communications between the distanced neural areas but are sensitive to the intensity variations of the optical signal. For systems with several neuromorphic sensors, which are connected optically to the main unit, the use of optical synapses is not an advantage. To address this, in this paper we propose and experimentally verify optical axons with synapses activated optically using digital signals. The synaptic weights are encoded by the energy of the stimuli, which are then optically transmitted independently. We show that the optical intensity fluctuations and link’s misalignment result in delay in activation of the synapses. For the proposed optical axon, we have demonstrated line of sight transmission over a maximum link length of 190 cm with a delay of 8 μs. Furthermore, we show the axon delay as a function of the illuminance using a fitted model for which the root mean square error (RMS) similarity is 0.95.

scholarly journals Generalized convolution theorem associated with fractional Fourier transform

2012 ◽  
Vol 14 (13) ◽  
pp. 1340-1351 ◽  
Author(s):  
Jun Shi ◽  
Xuejun Sha ◽  
Xiaocheng Song ◽  
Naitong Zhang
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Convolution Theorem ◽  
Generalized Convolution
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