In order to test the validity of the global wavelet spectrum - a new period analysis method based on wavelet analysis, we carried out some simple experiments. In our experiments we used idealized time series and real ...In order to test the validity of the global wavelet spectrum - a new period analysis method based on wavelet analysis, we carried out some simple experiments. In our experiments we used idealized time series and real Ni(~n)o 3 sea surface temperature (SST) for testing purposes. First we combined different signals which have the same power but different periods into some new time series. Then we calculated the global wavelet spectra and Fourier power spectra for the testing time series. The testing results revealed that on some occasions the global wavelet spectrum tends to amplify the relative power of longer periods. By making comparisons with the results obtained by the traditional Fourier power spectrum, we demonstrated that on an occasion when the global wavelet spectrum does not work the Fourier power spectrum can be used to achieve the right results. Hence it is recommended that when making period analysis with the global wavelet spectrum one needs to do further tests to confirm their results.展开更多
The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fra...The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.展开更多
Because of its all-reflective layout based on the Fresnel double-mirror interference system, the newly developed Fourier transform imaging spectrometer has a very large spectral bandwidth ranged from a cut-off wavelen...Because of its all-reflective layout based on the Fresnel double-mirror interference system, the newly developed Fourier transform imaging spectrometer has a very large spectral bandwidth ranged from a cut-off wavelength (related to the cut-off wave number σ max ) to far infrared. According to the signal's symmetry and wide-band characteristics, a simple method that can efficiently weaken the low frequency noise in the reconstructed spectrum is presented. Also, according to the symmetry, the eigenvector method is applied to the reconstruction of the spectrum.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grants 20475068)the Natural Science Foundation of Guangdong Province(Contact No.031577)the Opening Foundation of State Key Laboratory of Chem/Biosensing and Chemometrics of Hunan University(2003).
基金This study was suppo rted by a key program from the National Natural Science Foundation of China(NSFC)(Grant No.40233033).
文摘In order to test the validity of the global wavelet spectrum - a new period analysis method based on wavelet analysis, we carried out some simple experiments. In our experiments we used idealized time series and real Ni(~n)o 3 sea surface temperature (SST) for testing purposes. First we combined different signals which have the same power but different periods into some new time series. Then we calculated the global wavelet spectra and Fourier power spectra for the testing time series. The testing results revealed that on some occasions the global wavelet spectrum tends to amplify the relative power of longer periods. By making comparisons with the results obtained by the traditional Fourier power spectrum, we demonstrated that on an occasion when the global wavelet spectrum does not work the Fourier power spectrum can be used to achieve the right results. Hence it is recommended that when making period analysis with the global wavelet spectrum one needs to do further tests to confirm their results.
基金supported by National Natural Science Foundation of China(Grant Nos.51175085,51205062)Fujian Provincial Natural Science Foundation of China(Grant Nos.2011J01299,2012J01206)Development Foundation for Science and Technology of Fuzhou University,China(Grant No.2011-XY-10)
文摘The discrete Fourier transform（DFT） is used for fractional Brownian motion（FBM） surface synthesis in tribology（i.e., contact, sliding, and sealing, etc）. However, the relationship between fractal parameters（fractal dimension and scale factor） and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface （Sq） is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height（Sz）, the skewness（Ssk） and the kurtosis（Sku） are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.
文摘Because of its all-reflective layout based on the Fresnel double-mirror interference system, the newly developed Fourier transform imaging spectrometer has a very large spectral bandwidth ranged from a cut-off wavelength (related to the cut-off wave number σ max ) to far infrared. According to the signal's symmetry and wide-band characteristics, a simple method that can efficiently weaken the low frequency noise in the reconstructed spectrum is presented. Also, according to the symmetry, the eigenvector method is applied to the reconstruction of the spectrum.
