Nonlinear matched filtering and neural networks

A 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 are equivalent to three-layer neural nets. They have better performance in terms of signal discrimination than previously known filters. The matched filters are further subdivided into two major classes according to the DFT (discrete Fourier transform) or the RDFT-based filtering. DFT and RDFT are approximations to the complex and real Fourier transforms, respectively. The RDFT-based filtering gives better performance in terms of spatial resolution, intermediate noise, and signal discrimination than the DFT-based filtering.<>