An efficient recursive time-varying Fourier transform by using a half-sine wave window

Author(s):  
Weizhong Chen ◽  
N.C. Griswold
2013 ◽  
Vol 690-693 ◽  
pp. 2514-2518
Author(s):  
Juan Cong ◽  
Yun Wang ◽  
Wei Na Yu

Through the research on the change of system input and output energy in time-varying speed cutting, the influence of variable-speed waveforms on vibration suppression effect in time-varying speed cutting is quantitatively analyzed in this paper. A conclusion can be drawn that sine wave speed variation is better than triangle wave speed variation in vibration suppression.


PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0242147
Author(s):  
Emily M. Wong ◽  
Fern Tablin ◽  
Edward S. Schelegle

The aim of time-varying heart rate variability spectral analysis is to detect and quantify changes in the heart rate variability spectrum components during nonstationary events. Of the methods available, the nonparametric short-time Fourier Transform and parametric time-varying autoregressive modeling are the most commonly employed. The current study (1) compares short-time Fourier Transform and autoregressive modeling methods influence on heart rate variability spectral characteristics over time and during an experimental ozone exposure in mature adult spontaneously hypertensive rats, (2) evaluates the agreement between short-time Fourier Transform and autoregressive modeling method results, and (3) describes the advantages and disadvantages of each method. Although similar trends were detected during ozone exposure, statistical comparisons identified significant differences between short-time Fourier Transform and autoregressive modeling analysis results. Significant differences were observed between methods for LF power (p ≤ 0.014); HF power (p ≤ 0.011); total power (p ≤ 0.027); and normalized HF power (p = 0.05). Furthermore, inconsistencies between exposure-related observations accentuated the lack of agreement between short-time Fourier Transform and autoregressive modeling overall. Thus, the short-time Fourier Transform and autoregressive modeling methods for time-varying heart rate variability analysis could not be considered interchangeable for evaluations with or without interventions that are known to affect cardio-autonomic activity.


ACTA IMEKO ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 17
Author(s):  
Daniel Belega ◽  
Dario Petri ◽  
Dominique Dallet

<p class="Abstract">This article investigates the contribution of a small-amplitude interharmonic component to the sine-wave parameter estimators returned by the classical interpolated discrete Fourier transform (IpDFT) algorithm. The analytical expressions for the frequency, amplitude, and phase estimation errors are derived herein by considering the IpDFT algorithm based on the maximum sidelobe decay (MSD) windows and by assuming the interharmonic frequency located at least one bin apart the unknown sine-wave frequency. The derived expressions allow us to analyse the impact of an interharmonic on the accuracies of the IpDFT frequency, amplitude, and phase estimators. The accuracies of the derived expressions are verified by means of both computer simulations and experimental results.</p>


Author(s):  
Vincent Melot ◽  
Jean Franc¸ois Sigrist ◽  
Christian Laine ◽  
Bruno Auvity ◽  
Hassan Peerhossaini

The present paper deals with the study of fluid forces in an incompressible viscous fluid at rest around an accelerated rigid circular cylinder. The movement subjected to the cylinder is an impulsive motion represented by a only one period of a sinusoidal acceleration. After this period, the cylinder is stopped. This study is performed for small displacement of the cylinder, i.e. for low KEULEGAN-CARPENTER numbers, and for various STOKES numbers. An analytical formulation of fluid forces exerted on a cylinder subjected to any motion is first proposed. The starting point of the analytical approach is the solution of fluid forces in steady state harmonic motion. A Fourier transform is applied on the harmonic solution to capture the wide frequency spectrum composing the transient motion. Then an inverse Fourier transform is applied on the expression to achieve the solution in the temporal space. A numerical simulation is then carried out with a CFD code using finite volume method with moving mesh technique in ALE formulation. The analytical and numerical solutions are exposed and discussed in the case of a cylinder subjected to a sine wave acceleration. The competition between the viscous diffusion time and the wave duration time is studied and highlights the history effect on pressure forces and shear forces.


2002 ◽  
Vol 112 (5) ◽  
pp. 2358-2358
Author(s):  
Jyrki Tuomainen ◽  
Tobias Andersen ◽  
Kaisa Tiippana ◽  
Mikko Sams

2021 ◽  
pp. 106-155
Author(s):  
Victor Lazzarini

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.


Author(s):  
Fawzi M. A. El-Saeidy

Abstract An Analytical model is presented to simulate effect of tooth backlash on vibration spectrum of spur gearboxes incorporating sleeve bearings. Included in the model are: elasticity of shafts, friction between meshing teeth, interaction between gearbox casing and internals, and time-varying tooth backlash (backlash is a function of operating center distance), mesh stiffness (stiffness is calculated based on the strain energies of the tooth that is treated as a cantilever beam of involute shape) and Hertzian mesh damping. The bearing forces are calculated with consideration of bearing radial clearance and system vibrations. The analysis is applied to a single stage gearbox and equations of motion are numerically integrated to obtain system reponse in time domain. This response is transformed into frequency domain (vibration spectrum) using Fast Fourier Transform (FFT) algorithm and samples of the results are shown for different values of tooth backlash. The results show that backlash has a pronounced effect on gearbox vibration and study provides an analysis procedure for predicting such effects.


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