Frequency-domain design of N-D digital filters

This paper investigates the problem of designing
N-D (N > 2)
IIR digital filters. An
I_{p}
design technique for
N-D (N> 2)
IIR digital filters is proposed. The minimization technique described is a new adaptive parallel targent (PARTAN) method which requires only the computation of the first derivatives of the performance index. The stability of the resulting filter is shown to be guaranteed by limiting the coefficient variations at every iteration. Thus the testing for stability at the end of each iteration is considerably simplified. The computational complexity is further reduced by a table look-up method that utilizes the properties of the orthogonal sampling grid in the frequency domain. To illustrate the method, a three-dimensional general-support conic filter and a five-dimensional causal hyperspherical high-pass filter are designed.