Stability analysis of the second-order lossless digital integrator allpass filter

In this paper, the stability of the second-order LDI allpass filter is investigated. The stability is affected by the placement of the nonlinearities. Here, two cases are studied. The first when all nonlinearities are placed immediately before the delays, and the second when the quantizer is located after the adder which follows the multipliers. In first case, we study both zero-input limit cycles and forced response while the latter deals only with zero input quantization limit cycles. The results show that the filter in both cases is stable when the poles are located within a circle centered at z=0.39, touching z=1, provided that magnitude truncation and saturation or triangular overflow characteristics are used