Nonlinear matched filtering

Abstract

A new class of nonlinear matched filters is discussed. These filters involve the transformation of the signal spectrum and the filter transfer function through a nonlinearity before they are multiplied in the transform domain. The resulting filter structures can be considered to be analogous to three-layer neural nets. They have better performance in terms of signal discrimination and lack of false correlation signals and artifacts than previously known filters. The matched filters are further subdivided into two major classes according to whether the filtering is based on a discrete Fourier transform (DFT) or a real discrete Fourier transform (RDFT). The DFT and the RDFT are approximations to the complex and real Fourier transforms, respectively. The RDFT-based filtering gives better performance in terms of signal discrimination and lack of false correlation signals and artifacts than the DFT-based filtering.