不变子空间在周期解析信号中的应用

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。

Applications of the Backward Shift Invariant Subspace to Circular Analytic Signals

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 analytic is presented. Particularly, if the Z transform of the circular analytic signal is holomorphic across the unit 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.