On the Stability of Coupled-form State-space Digital Filters with Quantization before Summation

 The problem of suppressing zero-input limit cycles in coupled-form state-space digital filters when the quantization is performed just after the multiplication is here addressed. No proof has been presented guaranteeing that zero-input limit cycles are not sustained in the filter output when the poles are placed anywhere inside the unit circle. Some authors have addressed this topic, but the results in the literature constrain the poles to stay in a bounded region inside the unit circle. As a contribution to this discussion, this paper presents a proof of the stability of the second-order coupled-form filter whose poles are inside the unit circle in the direction of 0, ±45, ±90, ±135 or 180 degrees. This freedom of zero-input limit cycles, however, is guaranteed only if the quantizers perform magnitude truncation, as it happens in the case of quantizers applied to the state variables.