摘要
Suppose thatx=|x(n)|n∈? is a sequence of real numbers. For eachp∈?,x p =|x p (n)|n∈?is the resulting sequence ofx throughp times median filterings with window 2k+1. It is proved that whenp→∞, bothx (2p) andx(2 p}-1) are convergent. Thus the problem of convergence of the median filters of infinite-length sequences is completely solved.
Suppose that x={x（n）}<sub>n∈Z</sub> is a sequence of real numbers. For each p∈N, x<sup>（p）</sup>={x<sup>（p）</sup>（n）}<sub>n∈Z</sub> is the resulting sequence of x through p times median filterings with window 2k+1. It is proved that when p→∞, both x<sup>（2p）</sup> and x<sup>（2p-1）</sup> are convergent. Thus the problem of convergence of the median filters of infinite-length sequences is completely solved.
基金
Project supported by the National Natural Science Foundation of China (Grant No. 16971047)
