This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality w...This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.展开更多
This paper investigates the generalized uncertainty principles of fractional Fourier transform (FRFT) for concentrated data in limited supports. The continuous and discrete generalized uncertainty relations, whose bou...This paper investigates the generalized uncertainty principles of fractional Fourier transform (FRFT) for concentrated data in limited supports. The continuous and discrete generalized uncertainty relations, whose bounds are related to FRFT parameters and signal lengths, were derived in theory. These uncertainty principles disclose that the data in FRFT domains may have?much higher concentration than that in traditional time-frequency domains, which will enrich the ensemble of generalized uncertainty principles.展开更多
Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discr...Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.展开更多
The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the s...The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform（DFRFT）is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio（SNR）,and enhance the original speech signal.展开更多
Parameter estimation is analyzed using two kinds of common sampling-type DFRFT(discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation a...Parameter estimation is analyzed using two kinds of common sampling-type DFRFT(discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation accuracy are analyzed. And the simulation is made to verify the conclusions. From the theoretic analysis and simulation verification, it can be drawn that, for the estimation of chirp-rate and initial frequency, Pei's method [10] is more suitable if the absolute value of chirp-rate is small relatively; Ozaktas' method [9] is more suitable if the absolute value of chirp-rate is large relatively; and the two methods are both workable if the absolute value of chirp-rate is moderate. The scope of moderate chirp-rate can be approximately determined as [40 Hz/s, 110 Hz/s].展开更多
文摘This paper investigates the generalized Parseval’s theorem of fractional Fourier transform (FRFT) for concentrated data. Also, in the framework of multiple FRFT domains, Parseval’s theorem reduces to an inequality with lower and upper bounds associated with FRFT parameters, named as generalized Parseval’s theorem by us. These results theoretically provide potential valuable applications in filtering, and examples of filtering for LFM signals in FRFT domains are demonstrated to support the derived conclusions.
文摘This paper investigates the generalized uncertainty principles of fractional Fourier transform (FRFT) for concentrated data in limited supports. The continuous and discrete generalized uncertainty relations, whose bounds are related to FRFT parameters and signal lengths, were derived in theory. These uncertainty principles disclose that the data in FRFT domains may have?much higher concentration than that in traditional time-frequency domains, which will enrich the ensemble of generalized uncertainty principles.
文摘Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.
文摘The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform（DFRFT）is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio（SNR）,and enhance the original speech signal.
基金the National Natural Science Foundation of China (60902054)China Postdoctora Science Foundation (201003758, 20090460114) "Taishan Scholars" Special Foundation of Shandong Province for the support
文摘Parameter estimation is analyzed using two kinds of common sampling-type DFRFT(discrete fractional Fourier transform) algorithm. A model of parameter estimation is established. The factors which influence estimation accuracy are analyzed. And the simulation is made to verify the conclusions. From the theoretic analysis and simulation verification, it can be drawn that, for the estimation of chirp-rate and initial frequency, Pei's method [10] is more suitable if the absolute value of chirp-rate is small relatively; Ozaktas' method [9] is more suitable if the absolute value of chirp-rate is large relatively; and the two methods are both workable if the absolute value of chirp-rate is moderate. The scope of moderate chirp-rate can be approximately determined as [40 Hz/s, 110 Hz/s].
