The cascade algorithm plays an important role in computer graphics and wavelet analysis. For any initial function φn, a cascade sequence (φn)n∞=1 constructed by the iteration φn=Cnφn-1=1,2.. where Cαis defined b...The cascade algorithm plays an important role in computer graphics and wavelet analysis. For any initial function φn, a cascade sequence (φn)n∞=1 constructed by the iteration φn=Cnφn-1=1,2.. where Cαis defined by g∈Lp(R) In this paper, we characterize the convergence of a cascade sequence in terms of a sequence of functions and in terms of joint spectral radius. As a consequence, it is proved that any convergent cascade sequence has a convergence rate of geometry, i.e., ||φ+1-φn||Lp(R)=O((?)n)for some (?)∈(0.1i). The condition of sum rules for the mask is not required. Finally, an example is presented to illustrate our theory.展开更多
In order to provide a judicious pulse waveform design required for ultra-wideband(UWB)communication to enable the UWB spectral mask compatible and coexistent with other existing wireless communication systems,a semi-d...In order to provide a judicious pulse waveform design required for ultra-wideband(UWB)communication to enable the UWB spectral mask compatible and coexistent with other existing wireless communication systems,a semi-definite programming(SDP)based pulse waveform design method for UWB radios is introduced and a further analysis is given in this paper.By using Sedumi and Yalmip toolboxes of Matlab,the procedure of solving the SDP problem is simplified.Simulation results show that this SDP based pulse waveform design method can be used to design pulses that fulfill the Federal Communications Commission(FCC)spectral mask strictly and optimize the power efficiency at the same time.This paper also analyzes the influences of the power efficiency duing to the changes of sampling interval and the number of combined pulses,and then the optimal sampling interval that maximizes the transmission power can be found.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171007).
文摘The cascade algorithm plays an important role in computer graphics and wavelet analysis. For any initial function φn, a cascade sequence (φn)n∞=1 constructed by the iteration φn=Cnφn-1=1,2.. where Cαis defined by g∈Lp(R) In this paper, we characterize the convergence of a cascade sequence in terms of a sequence of functions and in terms of joint spectral radius. As a consequence, it is proved that any convergent cascade sequence has a convergence rate of geometry, i.e., ||φ+1-φn||Lp(R)=O((?)n)for some (?)∈(0.1i). The condition of sum rules for the mask is not required. Finally, an example is presented to illustrate our theory.
基金the National Natural Science Foundation of China (Grant No.60432040)Program for New Century Excellent Talents in University(Grant No.NCET-04-0332)
文摘In order to provide a judicious pulse waveform design required for ultra-wideband(UWB)communication to enable the UWB spectral mask compatible and coexistent with other existing wireless communication systems,a semi-definite programming(SDP)based pulse waveform design method for UWB radios is introduced and a further analysis is given in this paper.By using Sedumi and Yalmip toolboxes of Matlab,the procedure of solving the SDP problem is simplified.Simulation results show that this SDP based pulse waveform design method can be used to design pulses that fulfill the Federal Communications Commission(FCC)spectral mask strictly and optimize the power efficiency at the same time.This paper also analyzes the influences of the power efficiency duing to the changes of sampling interval and the number of combined pulses,and then the optimal sampling interval that maximizes the transmission power can be found.
