Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

• DOI: 10.1364/josaa.22.000917
• Publication Date: 2005-05-04T21:20:12Z
• Authors: Bryan M. Hennelly; John T. Sheridan
• Keywords: Wigner distribution function; Decimation

By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) a signal, as indicated by location signal energy in Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation described linear canonical transform. Then, applying regular uniform sampling criteria imposed SBP and linking explicitly to decomposition matrix system, numerical algorithms (employing interpolation decimation), which exhibit both invertibility additivity, implemented. Algorithms appearing literature for variety transforms (Fresnel, fractional Fourier) are special cases our general approach. The method allow existing optimized also permit invention many new algorithms.