scholarly journals Numerical evaluation of the Hilbert transform by the Fast Fourier Transform (FFT) technique

1981 ◽  
Vol 67 (3) ◽  
pp. 791-799 ◽  
Author(s):  
H.-P. Liu ◽  
D. D. Kosloff
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Hilbert Transform ◽  
Numerical Evaluation ◽  
The Hilbert Transform

The Analysis of Gearbox Fault Diagnosis Research Based on the EMD and Hilbert Envelope Demodulation

2014 ◽  
Vol 926-930 ◽  
pp. 1800-1805 ◽  
Author(s):  
Guo Dong Han ◽  
Shu Ting Wan ◽  
Zhan Jie Lv ◽  
Rong Hai Liu ◽  
Jin Wang ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fault Diagnosis ◽  
Power Spectrum ◽  
Fast Fourier Transform ◽  
Empirical Mode Decomposition ◽  
Hilbert Transform ◽  
Mode Decomposition ◽  
Signal Characteristics ◽  
The Hilbert Transform ◽  
Fault Characteristic

This paper puts forward a kind of gearbox fault diagnosis methods which based on empirical mode decomposition (EMD), Hilbert transform, Fast Fourier Transform (FFT) and spectrum refined techniques. This method is applicable to the analysis of the nonlinear unsteady signal. First of all used wavelet denoising to the acquisition of gearbox vibrate signal, again carries on the empirical mode decomposition (EMD), than get a certain number of intrinsic mode function (imf); Choose the specific imf, based on kurtosis value, after the Hilbert transform and Fast Fourier Transform is done, the corresponding power spectrum can be obtained; To refine the power spectrum and extract the gearbox fault characteristic frequency; Then in pattern recognition and diagnosis of the gearbox fault, and compared with the normal signal characteristics. The analysis results show that the proposed method can effectively detect the gearbox fault characteristics.

scholarly journals NONPARAMETRIC ANALYSES OF LOG-PERIODIC PRECURSORS TO FINANCIAL CRASHES

2003 ◽  
Vol 14 (08) ◽  
pp. 1107-1125 ◽  
Author(s):  
WEI-XING ZHOU ◽  
DIDIER SORNETTE
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Power Law ◽  
Hilbert Transform ◽  
Strong Evidence ◽  
Unpublished Report ◽  
Dow Jones Industrial Average ◽  
The Hilbert Transform ◽  
Financial Indices ◽  
Good Agreement

We apply two nonparametric methods to further test the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The term "parametric" refers here to the use of the log-periodic power law formula to fit the data; in contrast, "nonparametric" refers to the use of general tools such as Fourier transform, and in the present case the Hilbert transform and the so-called (H, q)-analysis. The analysis using the (H, q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln (tc-t) variable, where tcis the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequency f=1.02±0.05 corresponding to the scaling ratio λ=2.67±0.12. These values are in very good agreement with those obtained in earlier works with different parametric techniques. This note is extracted from a long unpublished report with 58 figures available at , which extensively describes the evidence we have accumulated on these seven time series, in particular by presenting all relevant details so that the reader can judge for himself or herself the validity and robustness of the results.

The properties of generalized offset linear canonical Hilbert transform and its applications

2017 ◽  
Vol 15 (04) ◽  
pp. 1750031 ◽  
Author(s):  
Shuiqing Xu ◽  
Li Feng ◽  
Yi Chai ◽  
Youqiang Hu ◽  
Lei Huang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Hilbert Transform ◽  
Analytic Signal ◽  
Linear Canonical Transform ◽  
Single Sideband ◽  
Generalized Hilbert Transform ◽  
Offset Linear Canonical Transform ◽  
The Fourier Transform ◽  
The Hilbert Transform

The Hilbert transform is tightly associated with the Fourier transform. As the offset linear canonical transform (OLCT) has been shown to be useful and powerful in signal processing and optics, the concept of generalized Hilbert transform associated with the OLCT has been proposed in the literature. However, some basic results for the generalized Hilbert transform still remain unknown. Therefore, in this paper, theories and properties of the generalized Hilbert transform have been considered. First, we introduce some basic properties of the generalized Hilbert transform. Then, an important theorem for the generalized analytic signal is presented. Subsequently, the generalized Bedrosian theorem for the generalized Hilbert transform is formulated. In addition, a generalized secure single-sideband (SSB) modulation system is also presented. Finally, the simulations are carried out to verify the validity and correctness of the proposed results.

Feasibility study of the Hilbert transform in detecting the gear rattle phenomenon of automotive transmissions

2017 ◽  
Vol 24 (12) ◽  
pp. 2631-2641 ◽  
Author(s):  
Renato Brancati ◽  
Ernesto Rocca ◽  
Davide Lauria
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Feasibility Study ◽  
Hilbert Transform ◽  
Experimental Tests ◽  
Feasibility Analysis ◽  
Mean Square ◽  
Optical Encoder ◽  
The Hilbert Transform ◽  
Gear Rattle

This paper describes the feasibility analysis of a methodology based on the Hilbert transform in order to detect the gear rattle phenomenon of automotive transmissions. The technique adopts the Hilbert transform to analyze experimental signals of the relative angular motion of gears starting from high-resolution optical encoder measurements. By this procedure it is possible to evaluate the severity of impacts occurring between the teeth of unloaded gears, by examining the root mean square value of the signal. The Hilbert transform is largely adopted in the detection of gear defects, such as tooth cracks, but it has not yet been used to detect gear rattle. This feasibility study highlights the capability in discriminating between impacts occurring on the two different sides of the tooth. The method puts in evidence the influence of oil lubricant between the teeth in reducing the severity of the impacts, by comparing many experimental tests performed with two different oils for transmission gears. Moreover, in order to evaluate the reliability of the proposed methodology some comparisons are conducted with a metric based on the fast Fourier transform, often adopted in this field, to highlight the goodness and simplicity of the technique based on the Hilbert transform.

A space of slowly decreasing functions with pleasant Fourier transforms

1991 ◽  
Vol 119 (1-2) ◽  
pp. 73-86
Author(s):  
L. E. Fraenkel
Keyword(s):  
Banach Space ◽  
Fourier Transform ◽  
Bounded Variation ◽  
Hilbert Transform ◽  
Fourier Transforms ◽  
Weighting Function ◽  
The Fourier Transform ◽  
The Hilbert Transform ◽  
Decreasing Functions

SynopsisThe space in question is Aµ(R):=L1(R) + Bµ(R), where Bµ(R) is a Banach space that contains the “tails” (the dominant parts for large values of |x|) of certain slowly decreasing functions from R to R. Functions in Bµ(R) are of bounded variation, and the norm involves their variation and a weighting function. Theorems are proved only for Bµ(R), because those for L1(R) are known. The results concern the convolution of a function in Bµ(R) with one in L1(R), the Fourier transform acting on Bµ(R), and the signum rule for the Hilbert transform of functions in Bµ(R).

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