NFIR nonlinear filter

A nonlinear filter is introduced whose output is nearest in distance to the output of a FIR (finite impulse response) linear phase filter; hence it is called the NFIR filter. After choosing the impulse response of the FIR filter properly, the NFIR filter can clean impulsive noise and preserve edges of signals. As a special case of the NFIR filter, a nearest mean (NEME) filter is derived. Theoretical analysis shows that the NEME filter is better than the median filter in smoothing additive Gaussian noise. In addition, based on the definition of the NEME filter, a new interpretation of the low-pass property of the median filter with window width 3 is described. Also, the performance of the nearest mean filter on a noisy edge is quantitatively compared with that of the median and mean filters