Abstract
This work aims to define Sonine filters and introduce them for digital image processing. Their fundamental properties are described and an optimizing performance procedure is explained, exploiting the unique advantage that this kind of filters possess, which consists of having simple analytical finite Fourier transforms for circular, elliptical and rectangular domains. A comparison with various existing filters is also presented, like Gaussian, Hann, Hamming, Blackmann, etc. Some relations are provided to facilitate their applicability. Also, comprehensive optimized filter designs are provided. Finally, an experimental application for intensity normalization and noise reduction of fringe patterns is described, showing that this kind of filters could be helpful in digital image processing and particularly in the analysis of fringe patterns.