The problem of reconstructing a signalφ（x） from its magnitude ｜φ（x）] isof considerable interest to engineers and physicists. This article concerns the problem of determining a time-limited signal f with period ...The problem of reconstructing a signalφ（x） from its magnitude ｜φ（x）] isof considerable interest to engineers and physicists. This article concerns the problem of determining a time-limited signal f with period 2π when ｜f（eix）l is known for x∈[-π,π]. It is shown that the conditions ｜g（eix）｜ = ｜f（eix）｜ and ｜g（ci（x＋b）） -g（eix）｜ =f（ei（x＋b）） - f（eix）｜, b ≠ 27π, together imply that either g = wf or g = v f, where both w and v have period b. Furthermore, if b/2π is irrational then the functions w and v b is rational then w takes the form reduce to some constants c1 and c2, respectively; ifb/2π is rational then w takes the form w=elexB1（e1x）B2（elx）and v takes the form ei（x2πN/b＋a）B1（elx）B2（elx）,where B1 and B2 are Blaschke products.展开更多
Optical transmission technologies have gone through several generations of development.Spectral efficiency has significant ly improved,and industry has begun to search for an answer to a basic question：What are the f...Optical transmission technologies have gone through several generations of development.Spectral efficiency has significant ly improved,and industry has begun to search for an answer to a basic question：What are the fundamental linear and nonlin ear signal channel limitations of the Shannon theory when there is no compensation in an optical fiber transmission system？Next-generation technologies should exceed the 100G transmis sion capability of coherent systems in order to approach the Shannon limit.Spectral efficiency first needs to be improved be fore overall transmission capability can be improved.The means to improve spectral efficiency include more complex modulation formats and channel encoding/decoding algorithms,prefiltering with multisymbol detection,optical OFDM and Ny quist WDM multicarrier technologies,and nonlinearity compen sation.With further optimization,these technologies will most likely be incorporated into beyond-100G optical transport sys tems to meet bandwidth demand.展开更多
We propose a low complexity iterative algorithm for band limited signal extrapolation. The extrapolation method is based on the decomposition of finite segments of the signal via truncated series of real-valued linear...We propose a low complexity iterative algorithm for band limited signal extrapolation. The extrapolation method is based on the decomposition of finite segments of the signal via truncated series of real-valued linear prolate functions. Our theoretical derivation shows that given a truncated series (up to a selectable value) of prolate functions, it is possible to extrapolate the band limited function elsewhere if each extrapolated portion of the function is subject only to moderate truncation errors that we quantify in this paper. The effects of different sources of errors have been analyzed via extensive simulations. We have investigated a property of the signal decomposition formula based on linear prolate functions whereby the integration interval does not need to be symmetric with respect to the origin while time-shifted prolate functions are used in the series.展开更多
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, based on the Kavaya-Suni format, discusses the signal-to-noise ratio equation of the diffraction-limited coherent CO 2 lidar in detail, which is applied to atmospheric turbulence. The cumulative SNR and r...This paper, based on the Kavaya-Suni format, discusses the signal-to-noise ratio equation of the diffraction-limited coherent CO 2 lidar in detail, which is applied to atmospheric turbulence. The cumulative SNR and relative SNR, which are all affected by the nonlinear effects of the diffraction-limited Gaussian beam, atmospheric molecule and atmospheric turbulence, are simulated by microcomputer. Six instructions for the optimal design of IR CO 2 Coherent Lidar System, are provided.展开更多
基金Supported by Foundation of Hubei Educational Committee (Q20091004)NSFC (10771053)+1 种基金the National Research Foundation for the Doctoral Program of Higher Education of China (SRFDP) (20060512001)Natural Science 373 Foundation of Hubei Province (2007ABA139)
文摘The problem of reconstructing a signalφ（x） from its magnitude ｜φ（x）] isof considerable interest to engineers and physicists. This article concerns the problem of determining a time-limited signal f with period 2π when ｜f（eix）l is known for x∈[-π,π]. It is shown that the conditions ｜g（eix）｜ = ｜f（eix）｜ and ｜g（ci（x＋b）） -g（eix）｜ =f（ei（x＋b）） - f（eix）｜, b ≠ 27π, together imply that either g = wf or g = v f, where both w and v have period b. Furthermore, if b/2π is irrational then the functions w and v b is rational then w takes the form reduce to some constants c1 and c2, respectively; ifb/2π is rational then w takes the form w=elexB1（e1x）B2（elx）and v takes the form ei（x2πN/b＋a）B1（elx）B2（elx）,where B1 and B2 are Blaschke products.
基金supported by National High-Tech Research and Development Program of China under Grant No.2013AA010501
文摘Optical transmission technologies have gone through several generations of development.Spectral efficiency has significant ly improved,and industry has begun to search for an answer to a basic question：What are the fundamental linear and nonlin ear signal channel limitations of the Shannon theory when there is no compensation in an optical fiber transmission system？Next-generation technologies should exceed the 100G transmis sion capability of coherent systems in order to approach the Shannon limit.Spectral efficiency first needs to be improved be fore overall transmission capability can be improved.The means to improve spectral efficiency include more complex modulation formats and channel encoding/decoding algorithms,prefiltering with multisymbol detection,optical OFDM and Ny quist WDM multicarrier technologies,and nonlinearity compen sation.With further optimization,these technologies will most likely be incorporated into beyond-100G optical transport sys tems to meet bandwidth demand.
文摘We propose a low complexity iterative algorithm for band limited signal extrapolation. The extrapolation method is based on the decomposition of finite segments of the signal via truncated series of real-valued linear prolate functions. Our theoretical derivation shows that given a truncated series (up to a selectable value) of prolate functions, it is possible to extrapolate the band limited function elsewhere if each extrapolated portion of the function is subject only to moderate truncation errors that we quantify in this paper. The effects of different sources of errors have been analyzed via extensive simulations. We have investigated a property of the signal decomposition formula based on linear prolate functions whereby the integration interval does not need to be symmetric with respect to the origin while time-shifted prolate functions are used in the series.
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, based on the Kavaya-Suni format, discusses the signal-to-noise ratio equation of the diffraction-limited coherent CO 2 lidar in detail, which is applied to atmospheric turbulence. The cumulative SNR and relative SNR, which are all affected by the nonlinear effects of the diffraction-limited Gaussian beam, atmospheric molecule and atmospheric turbulence, are simulated by microcomputer. Six instructions for the optimal design of IR CO 2 Coherent Lidar System, are provided.
