A new optimization approach to the design of one-dimensional and two-dimensional finite impulse response digital filters
The theory for designing finite impulse response (FIR) frequency sampling digital filters can be extended to two-dimensions. The linear phase frequency response can be represented as a linear combination of individual frequency responses corresponding to the filter's bands. The design of two-dimensional frequency sampling filters (FSF) has been treated in the past by using the technique of linear programming to find the optimal values of the transition samples. Although in theory the method guarantees an optimal solution, convergence problems occurred; This paper will introduce some detail of a one-dimensional FSF design technique and then extend these concepts to the two-dimensional problem. The mean of the squared error in both the stopband and the passband is minimized subject to constraints on the filter's stopband. The filter's coefficients can be calculated by solving a linear system of equations.
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