The invention relates to the technical field of filters, and discloses a novel universal Legendre filter, which is implemented by the following steps of: S1, receiving and digitalizing a signal; s2, constructing a universal Legendre filter tap and a weight vector; s3, carrying out simplified implementation of only reserving a near-core item on the filter in the S2; s4, initializing the weight vector in the S2; s5, outputting a universal Legendre filter; and S6, performing weight coefficient initialization on the filter in S5 by using an adaptive weight updating algorithm. Compared with the prior art, the method not only comprises Legendre function extension terms, but also comprises cross terms formed by the Legendre function terms and simplified implementation forms of the cross terms, and meanwhile, an initialization method of two weight coefficients is provided in the adaptive algorithm, so that the adaptive algorithm has stronger nonlinear approximation and processing capabilities.