 However, for filters of moderate order another method can be used which justifies the design using transformation.Consider the equation for a 2-dimensional case,

formula_220

where,formula_221 is a Chebyshev polynomial.These polynomials are defined as,

formula_222

formula_223

formula_224

Using this we can form a digital network to realize the 2-D frequency response as shown in the figure below.Replacing x by formula_225 we get,

formula_226
Since each of these signals can be generated from two lower order signals, a ladder network of N outputs can be formed such that frequency response between the input and nth output is formula_227 .By weighting these outputs according to the equation mentioned below, The filter formula_215 can be realized.formula_229

This realization is as shown in the figure below.In the figure,the filters F define the transformation function and h(n) is the impulse response of the 1-D prototype filter .