| In the design and implementation of digital filters, stability and finite wordlength effects of digital filters are important issues. During the past two decades, periodically shift varying (PSV) digital filters have received widespread attention and have become very useful in signal processing. The design and implementation of PSV digital filters have been investigated to some extent. However, the stability and finite wordlength effects of PSV filters have not received much attention.; This thesis focuses on the stability of one-dimensional (1-D) and two-dimensional (2-D) linear PSV digital filters, with and without finite wordlength effects. In 1-D PSV filters, the effect of two's complement truncation (TCT) quantization and two's complement overflow are analyzed by using block-form and standard-form implementations. 2-D PSV digital filters formulated in state-space form are studied for stability and finite wordlength effects. Lyapunov energy functions are used for analysis. Several sufficient conditions and necessary conditions are established for the stability of 2-D PSV filters.; This thesis also studies some applications of 2-D PSV state-space filters. When multiplierless filters are implemented in VLSI, they provide several advantages such as higher speed, lower cost, more compact, and lower power consumption when compared to filters with multipliers. This provides the motivation for designing multiplierless filters. A new design of 2-D multiplierless digital filters is proposed which employs 2-D PSV state-space filters. The stability conditions established in this thesis are incorporated in the design process. The results of this thesis culminate in an application involving Differential Pulse Code Modulation (DPCM). A 2-D multiplierless DPCM system is designed for image compression which yields promising results. |
