 In general, the IIR frequency response can be expressed as

formula_276

where formula_277 and formula_278 are M-D finite extent coefficient arrays.The ratio is normalized so that formula_279

Now, let formula_280 represent the spectrum of a M-D input signal formula_84 and formula_90 represent the spectrum of a M-D output signal formula_83.formula_284

where formula_285 is a trigonometric polynomial defined as formula_286

In the signal domain, the equation becomes 
formula_287

After making an initial guess, and then substituting the guess in the above equation iteratively, a better approximation of formula_83 can be obtained –
formula_289

where formula_290 denotes the iteration index

In the frequency domain, the above equation becomes 
formula_291

An IIR filter is BIBO stable if formula_292

If we assume that formula_293 then

formula_294

Thus, it can be said that, the frequency response formula_88 of a M-D IIR filter can be obtained by infinite number of M-D FIR filtering operations.