The quaternion Fourier transform plays a vital role in the representation of two-dimensional signals. This paper characterizes spectrum of quaternion-valued signals on the quaternion Fourier transform domain by the pa...The quaternion Fourier transform plays a vital role in the representation of two-dimensional signals. This paper characterizes spectrum of quaternion-valued signals on the quaternion Fourier transform domain by the partial derivative.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
Most image saliency detection models are dependent on prior knowledge and demand high computational cost. However, spectral residual（SR） and phase spectrum of the Fourier transform（PFT） models are simple and fast ...Most image saliency detection models are dependent on prior knowledge and demand high computational cost. However, spectral residual（SR） and phase spectrum of the Fourier transform（PFT） models are simple and fast saliency detection approaches based on two-dimensional Fourier transform without the prior knowledge. For seismic data, the geological structure of the underground rock formation changes more obviously in the time direction. Therefore, one-dimensional Fourier transform is more suitable for seismic saliency detection. Fractional Fourier transform（FrFT） is an improved algorithm for Fourier transform, therefore we propose the seismic SR and PFT models in one-dimensional FrF T domain to obtain more detailed saliency maps. These two models use the amplitude and phase information in FrFT domain to construct the corresponding saliency maps in spatial domain. By means of these two models, several saliency maps at different fractional orders can be obtained for seismic attribute analysis. These saliency maps can characterize the detailed features and highlight the object areas, which is more conducive to determine the location of reservoirs. The performance of the proposed method is assessed on both simulated and real seismic data. The results indicate that our method is effective and convenient for seismic attribute extraction with good noise immunity.展开更多
A novel spectral representation based on fractional Fourier transform （FrFT） is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart...A novel spectral representation based on fractional Fourier transform （FrFT） is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart, and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart, and the better performance can be achieved if adaptive orders are used.展开更多
A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the rec...A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and bit-error-ratio (BER) are obtained.展开更多
文摘The quaternion Fourier transform plays a vital role in the representation of two-dimensional signals. This paper characterizes spectrum of quaternion-valued signals on the quaternion Fourier transform domain by the partial derivative.
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.
基金supported by the National Natural Science Foundation of China (Nos.61571096,61775030,41274127,41301460,and 40874066)
文摘Most image saliency detection models are dependent on prior knowledge and demand high computational cost. However, spectral residual（SR） and phase spectrum of the Fourier transform（PFT） models are simple and fast saliency detection approaches based on two-dimensional Fourier transform without the prior knowledge. For seismic data, the geological structure of the underground rock formation changes more obviously in the time direction. Therefore, one-dimensional Fourier transform is more suitable for seismic saliency detection. Fractional Fourier transform（FrFT） is an improved algorithm for Fourier transform, therefore we propose the seismic SR and PFT models in one-dimensional FrF T domain to obtain more detailed saliency maps. These two models use the amplitude and phase information in FrFT domain to construct the corresponding saliency maps in spatial domain. By means of these two models, several saliency maps at different fractional orders can be obtained for seismic attribute analysis. These saliency maps can characterize the detailed features and highlight the object areas, which is more conducive to determine the location of reservoirs. The performance of the proposed method is assessed on both simulated and real seismic data. The results indicate that our method is effective and convenient for seismic attribute extraction with good noise immunity.
基金Sponsored by the National Natural Science Foundation of China(60605015)
文摘A novel spectral representation based on fractional Fourier transform （FrFT） is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart, and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart, and the better performance can be achieved if adaptive orders are used.
文摘A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and bit-error-ratio (BER) are obtained.
