| viXra.org > Functions and Analysis > 2407 |
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| viXra.org > Functions and Analysis > 2407 |
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[3] viXra:2407.0145 [pdf] submitted on 2024-07-24 00:54:29
Authors: Jon Un Song, Kwon Ryong Il
Comments: 8 Pages.
In general the sliding discrete Fourier transform (SDFT) for analyzing the frequency characteristics of shift data is not applied to the windowed shift data and so in this case a lot of calculations are needed. But in practical applications calculating the spectrum of the windowed shift data efficiently is needed.This paper proposes a SDFT of the windowed shift data using the window functions. Window functions have the symmetric property. Using this symmetric property, discrete Fourier transform (DFT) of the windowed shift data can be calculated by recursive algorithm.And this paper verifies its correctness and analyzes the number of calculations through the simulation using MATLAB. Several window functions, i.e. Bartlett, hanning, hamming, Blackman window functions are used to prove the proposed algorithm. These algorithms can be efficiently used in the analysis of frequency characteristics of the shift data and implemented using dsPIC, ARM and FPGA.
Category: Functions and Analysis
[2] viXra:2407.0134 [pdf] submitted on 2024-07-23 15:22:00
Authors: Yudai Sakuma
Comments: 4 Pages.
It is known that most of the formulae that hold for ordinary trigonometric functions hold for generalised trigonometric functions. In this study, we succeeded in generalizing lim(x→0)u2061(x/sinu2061x)=1 . This makes it possible to discuss the generalised case in unsolved problems involving trigonometric functions, such as the generalisation of the Flint Hills series.
Category: Functions and Analysis
[1] viXra:2407.0069 [pdf] submitted on 2024-07-10 17:33:14
Authors: Bertrand Wong
Comments: 2 Pages.
The motion of fluids which are incompressible could be described by the Navier-Stokes differential equations. Although they are relatively simple-looking, the three-dimensional Navier-Stokes equations misbehave very badly. Even with nice, smooth, reasonably harmless initial conditions, the solutions could wind up being extremely unstable. The field of fluid mechanics would be dramatically altered through a mathematical understanding of the outrageous behavior of these equations. The three-dimensional Navier-Stokes equations are apparently not solvable, i.e., the equations cannot be used to model turbulence or chaos (which is a three-dimensional phenomenon).
Category: Functions and Analysis
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