Patent Document ID: 20050111748
Application ID: 10717824
Patent Status: 0

Claim One:
1. A method for designing filters that approximates the circularly symmetric frequency response achievable using a non-separable filter comprising: (a) selecting a cut-off frequency and designing therefrom a 1-D low pass filter LP such that: LP=[X −n , X −(n-1) ,. .. X 0 ,. .. X n-1 , X n ; (b) obtaining a 2-D filter LPP by performing the operation: LP* X LP wherein LP* is a column vector having the same entries as LP and LPP having dimensions given by: {2n+1, 2n+1} and generating a 2-D countour plot therefor; (c) designing a 1-D high pass filter HP such that: HP=[Y −m , Y −(m-1) ,. .. Y 0 ,. .. Y m-1 , Y m ]; (d) obtaining a 2-D filter HPP by performing the operation: HP* X HP wherein HP* is a column vector having the same entries as HP and HPP having dimensions: {2m+1, 2m+1} and obtaining a 2-D contour plot therefor; (e) repeating (c) through (d) until the 2-D contour plot of HPP overlaps the 2-D countour plot of LPP; (f) generating a 2-D filter ONE having the dimensions of that of HPP with the only non-zero entry of value 1 located at the center of ONE; (g) creating matrix HPPinv by subtracting HPP from ONE; (h) convolving LPP with HPPinv to obtain DSCRN having dimensions: {2m+2n+1, 2m+2n+1} and obtaining a 2-D contour plot therefor; and (i) repeating (a) through (h) until, by an examination of the 2-D contour plot of DSCRN, an approximation to a desired circular symmetry is achieved.