中山大学学报(自然科学版)
中山大學學報(自然科學版)
중산대학학보(자연과학판)
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS SUNYATSENI
2013年
3期
63-66,72
,共5页
周期解析信号%共轭周期解析信号%后移不变子空间%幅度不变
週期解析信號%共軛週期解析信號%後移不變子空間%幅度不變
주기해석신호%공액주기해석신호%후이불변자공간%폭도불변
circular analytic signals%conjugate circular analytic signals%backward shift invariant sub-space%amplitude preservation
利用后移不变子空间,给出了周期解析信号与共轭周期解析信号的乘积仍为周期解析信号的充要条件。特别地,当周期解析信号对应的Z变换过圆周解析时,其对应的共轭周期解析信号为有理函数且有理函数的极点恰为周期解析信号对应的Z变换的零点。作为上述结论的应用,考虑了具有长度为n的Fourier级数的周期解析信号保持幅度不变的条件。
利用後移不變子空間,給齣瞭週期解析信號與共軛週期解析信號的乘積仍為週期解析信號的充要條件。特彆地,噹週期解析信號對應的Z變換過圓週解析時,其對應的共軛週期解析信號為有理函數且有理函數的極點恰為週期解析信號對應的Z變換的零點。作為上述結論的應用,攷慮瞭具有長度為n的Fourier級數的週期解析信號保持幅度不變的條件。
이용후이불변자공간,급출료주기해석신호여공액주기해석신호적승적잉위주기해석신호적충요조건。특별지,당주기해석신호대응적Z변환과원주해석시,기대응적공액주기해석신호위유리함수차유리함수적겁점흡위주기해석신호대응적Z변환적영점。작위상술결론적응용,고필료구유장도위n적Fourier급수적주기해석신호보지폭도불변적조건。
By use of the backward shift invariant subspace , a necessary and sufficient condition under which a product of a circular analytic signal and a conjugate circular analytic signal is still circular analyt -ic is presented.Particularly, if the Z-transform of the circular analytic signal is holomorphic across the u-nit circle, the conjugate circular analytic signal is a rational function whose poles are the zeros of the Z -transform of the circular analytic signal .As applications of the above results , the conditions under which two circular analytic signals with length n Fourier series have the same amplitude are discussed .