Asymptotic stability of digital filters with combinations of overflow and quantization nonlinearities

Using the BIBO (bounded-input, bounded-output) properties of nonlinear discrete systems, the problem of global asymptotic stability of nonlinear difference equations is investigated. The results have been applied to digital filters with a combination of quantization and overflow nonlinearities. Furthermore, the stability of two's complement arithmetic (quantization and overflow) has been treated. The strength of this approach lies in its ability to treat any combination of overflow and quantization nonlinearities. Thus it can guarantee global asymptotic stability of the digital filter by excluding any limit cycles due to these nonlinearities. This method can be applied to general-order direct form digital filters by using previously reported exact stability regions for quantization nonlinearities only.<>