Criteria for Limit Cycle Free State Space Digital Filters with External Disturbance

Abstract

Design and analysis of digital filters have received significant attention over the past few decades owing to their great importance in the field of engineering. Today, there is an ever-increasing number of applications that make use of digital filters or digital signal processing (DSP) algorithms in general. In any kind of electronic equipment, analog functions have been increasingly replaced by digital algorithms. This is true for instance for audio and video equipment, for communication, control and radar systems and in medical applications. newlineWhen a digital filter is realized on a fixed-point digital signal processors or special purpose hardware, one commonly come across with quantization and overflow nonlinearities. Owing to these nonlinearities, so-called limit cycles can occur which may seriously limit the application of digital filters in practice. Hence, the presence of these nonlinearities may lead to instability of the designed system. In general, quantization and overflow are not only conceptually decoupled, but also analytically treated as independent effects. The common types of overflow nonlinearities are saturation, zeroing, two s complement and triangular. These overflow nonlinearities together called as generalized overflow nonlinearities. newlineReal physical systems are usually corrupted by external disturbance because implementation of a high-order filter is usually done by serial arrangement of several low-order filters and external interference among these low-order digital filters is unavoidable. The occurrence of such external interferences or disturbances may cause malfunction and destruction phenomenon in the realized filter. Therefore, while designing the digital filters the designer should have a criterion for choosing the values of the filter coefficients which ensures the realized filter is free from limit cycles and the effect of external disturbance has to be minimized. newline