From phase space to frequency domain: A time-frequency analysis for chaotic time series

2007 ◽  
Vol 76 (1) ◽  
Author(s):  
Junfeng Sun ◽  
Yi Zhao ◽  
Tomomichi Nakamura ◽  
Michael Small
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Frequency Domain ◽  
Frequency Analysis ◽  
Chaotic Time Series ◽  
Time Frequency Analysis ◽  
Time Frequency

Extracting of Micro Doppler Parameter of Helicopter Rotor Based on Time-Frequency Analysis

2011 ◽  
Vol 130-134 ◽  
pp. 2696-2700 ◽  
Author(s):  
Lei Zhang ◽  
Guo Qing Huang
Keyword(s):  
Frequency Domain ◽  
Frequency Analysis ◽  
Time Domain ◽  
Good Method ◽  
Helicopter Rotor ◽  
Echo Signal ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Radar Echo ◽  
Doppler Parameter

The micro Doppler effect of the radar echo signal of helicopter rotor is studied, and the formula of helicopter rotor echo is obtained. Then the received echo signal of helicopter rotor simulated is analyzed in time domain, frequency domain and time-frequency domain respectively, the analysis results show that it is a good method to extract micro Doppler of helicopter rotor echo by time-frequency analysis. According to analysis results, obtained a method to determine parity of blades and velocity of helicopter rotor, these methods can be used to identify helicopter.

scholarly journals TIME-FREQUENCY ANALYSIS OF CLASSICAL TRAJECTORIES OF POLYATOMIC MOLECULES

2001 ◽  
Vol 11 (05) ◽  
pp. 1359-1380 ◽  
Author(s):  
LUZ V. VELA-AREVALO ◽  
STEPHEN WIGGINS
Keyword(s):  
Phase Space ◽  
Frequency Analysis ◽  
Degrees Of Freedom ◽  
First Integral ◽  
Complete Characterization ◽  
Global Dynamics ◽  
Time Frequency Analysis ◽  
Frequency Space ◽  
Time Frequency ◽  
Frequency Map

We present a new method of frequency analysis for Hamiltonian Systems of 3 degrees of freedom and more. The method is based on the concept of instantaneous frequency extracted numerically from the continuous wavelet transform of the trajectories. Knowing the time-evolution of the frequencies of a given trajectory, we can define a frequency map, resonances, and diffusion in frequency space as an indication of chaos. The time-frequency analysis method is applied to the Baggott Hamiltonian to characterize the global dynamics and the structure of the phase space in terms of resonance channels. This 3-degree-of-freedom system results from the classical version of the quantum Hamiltonian for the water molecule given by Baggott [1988]. Since another first integral of the motion exists, the so-called Polyad number, the system can be reduced to 2 degrees of freedom. The dynamics is therefore simplified and we give a complete characterization of the phase space, and at the same time we could validate the results of the time-frequency analysis.

Time-frequency analysis of fetal heartbeat fluctuation using wavelet transform

1998 ◽  
Vol 275 (6) ◽  
pp. H1993-H1999 ◽  
Author(s):  
Yoshitaka Kimura ◽  
Kunihiro Okamura ◽  
Takanori Watanabe ◽  
Nobuo Yaegashi ◽  
Shigeki Uehara ◽  
...  
Keyword(s):  
Heart Rate ◽  
Time Series ◽  
Wavelet Transform ◽  
Gamma Distribution ◽  
Frequency Analysis ◽  
Fetal Heart Rate ◽  
Fetal Heart ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Rate Fluctuation

We examined whether the nonlinear control mechanism of the fetal autonomic nervous system would change in various fetal states. Eight thousand or more fetal heartbeats were detected from normal, hypoxemic, and acidemic fetuses. Fetal heart Doppler-signal intervals were determined in a high-precision autocorrelation method, and a time series of fetal heart rate fluctuation was obtained. The distribution of the amplitude of temporal fluctuation in the low-frequency component of fetal heart rate frequency was studied using a method of time-frequency analysis called wavelet transform. Spline 4 was used as the mother wavelet function. A gamma distribution was observed from 17 wk of gestation onward. The value of the parameter ν of this gamma distribution was ∼1.6 and remained constant regardless of the gestational age or the time of day. The value of ν decreased significantly to 0.77 when the fetus developed acidemia and was 1.51 in hypoxemia and 1.54 in a normal condition. This study elucidates a nonlinear structure of the time series of heart rate fluctuation of the gamma distribution in the human fetus. This technique may provide a new quantitative index of fetal monitoring to diagnose fetal acidemia.

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