Under the Wiener least mean square （LMS） criteria

the performance of an adaptive noise cancelling filter is considered. Using the solution of optimum transfer function in frequency domain

we prove the limit cancelling ability and system gain are proportional with 1/τ

where τ is the correlation radius between input noise. The elementary conditions that must be satisfied in application of noise cancelling are given.In time domain

a transverse filter can approximate the optimum linear system with arbitrary accuracy. The representation of their relation is given. The results given in this paper can be easily applied to adaptive beamforming systems.A method （which is based on the inverse matrix of cross-power density spectrum） for calculating the ability of adaptive beamforming system to reject planar interference is given. A block diagram of system simulation by computer and some experimental results are shown at the end of the paper.