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文献[1]指出,为了保证超稳定自适应递归滤波器(HARF)的收敛性,传输函数必须满足严格正实(SPR)条件。在大量的实时应用中,要完全满足这种SPR条件是相当困难的。若能设法减弱、甚至消去这种苛求,势必会扩大自适应递归滤波器的使用范围。本文证明了,如果输入序列的平方和在任何时刻都有下界,HARF中可以完全消去这种SPR条件,并不影响其收敛性。最后,本文还给出了一些计算机模拟结果。
In [1], it is pointed out that in order to guarantee the convergence of the ultra stable adaptive adaptive recursive filter (HARF), the transfer function must satisfy the strict positive real (SPR) condition. In a large number of real-time applications, to fully meet the SPR conditions is quite difficult. If we can try to weaken or even eliminate this demanding, it is bound to expand the use of adaptive recursive filter. This paper proves that if the square sum of the input sequence has a lower bound at any moment, this SPR condition can be completely canceled in HARF without affecting its convergence. Finally, some computer simulation results are given.