VLSI architectures for real-time recursive state-space filtering. - Zhang, Jin Yun. (University of Ottawa (Canada), 1991)
The increasing demands of speed and performance become evident with the expanding utilization of signal/image processing to industrial, medical, and military environments. As the numerical properties are considered, state-space structures have been successfully exploited in realizing high performance fixed-point digital filters. However, they require more computations than other realizations. In this thesis, a general design methodology for mapping recursive algorithms onto optimal VLSI array processors is first given. Then, the parallel computational models for recursive state-space filtering are developed, and various high speed VLSI array architectures are obtained based on the design methodology. For 1-D IIR filters, the state variable representation is used to obtain a simple systolic array. Based on a block processing technique, an advanced state update algorithm is developed and a corresponding high speed array processor results for state-space filtering. By using the decomposition method, a cascade form of second-order state-space structures is suggested, which gives a high throughput rate and high efficiency with hardware less than for the Nth order form. In the 2-D case, besides the advanced state update array (called local speedup), the inherent spatial concurrency in 2-D systems is explored and a global speedup architecture is presented. This architecture consists of a number of column array processors and it works on multiple columns in parallel. It is very flexible and modular. The throughput rate is adjustable and therefore can be very high. In order to utilize the advantages of state-space filtering, the adaptive state-space filtering is developed based on the LMS algorithm. Gradients are derived directly from the state update equation and the observation equation. The stability monitoring, convergence rate and roundoff noise performance of the adaptive filter are studied. A VLSI architecture is proposed for speeding up the filtering and the adaptation. Finally, a very fast Kalman filter for image restoration is investigated. By using Roesser's LSS structure to represent the image generation model and the degradation model, a simple composite dynamic system representation is obtained. The fast Kalman filter is established by defining a proper state vector and using diagonal scanning method. A dedicated VLSI array architecture is designed for real-time image restoration. Proposed algorithms and architectures are verified by computer simulations.
Keywords: Engineering, Electronics and Electrical.