On Parametric Design And Efficient Implementation Of Digital Filters

Digital signal processing(DSP), as an interdiscipline subject of science and engineering, is one of the most important cornerstones for modern science and technology development, and has been applied in a wide range of scientific research and applications. Digital filter plays an important role in DSP systems and the design and implementation of digital filters are important research areas.Based on the state space theory, there exist a number of different structures for a digital filter and these structures are all equivalent in infinite precision implementation since they represent the same transfer function. Infinite precision design for digital filters pays attention to the efficiency of finding feasible solution and the stability of the system, finite precision design should further consider low complexity and finite word length effect of the structure. On the other hand, the digital filter can be implemented in two ways, the high throughput of the algorithm is mainly considered when implemented in computer software,high speed and low cost are key considerations while a well-designed filter is implemented with a digital device such as application specific integrated circuit and universal integrated circuit. In order to enhance the performance of digital systems, this thesis focuses on parametric design and efficient implementation of digital filters based on the theory of system structures. The main contributions are summarized as follows.1. A novel JSS structure based parametric IIR digital filter design: The cost function for designing IIR filter is highly nonlinear, and it is also constrained to the stability of the filter. JSS structure of an analog filter has only 2N + 1 parameters for an N th order filter and also has the property of l2-scaling. Based on the JSS structure and the generalized bilinear transformation, a new parameterization for designing stable IIR digital filter is proposed. This parameterization is complete and compact, which leads to a better convergence performance. Its corresponding stability region is the entire parameter space and hence the design can be carried out using well-established unconstrained nonlinear optimization methods. This parameterization designs stable IIR filter with a higher efficient,and enjoys better performance such as passband ripple, stopband attenuation and group delay.2. Discrete coefficient IIR digital filter design based on a lattice structure with genetic algorithm: A tapped numerator and injected numerator hybrid new lattice filter structure has degrees of freedom, and can be optimized for finite word length performance such as power ratio across signal nodes. This new lattice structure has only 2N + 1 multipliers and very low parameter sensitivity, which is especially suitable for discrete design of IIR filters. However, this kind of problems cannot be solved efficiently by using traditional gradient-based optimization techniques, and exhaustive search is unaffordable for solving the involved optimization problem because of large parameter search space. An efficient gray-based genetic algorithm is proposed to attack the nonlinear optimal problem.The global optimization is adopted for low order filters, and the step by step optimization is adopted for high order filters. The proposed method effectively finds a good balancing between performance and efficiency in the discrete design problems of IIR filters and is conducive to the practical application of IIR digital filter.3. Parallel computing digital filter structures for allpass systems: The inputbalance realizations have very nice numerical properties such as low sensitivity and small roundoff noise gain. Two classes of parallel computing digital filter structures for allpass systems are proposed based on a Hessenberg-based input-balance realization and normalized lattice structure. Based on the state-space approach, the principle of parallel processing is analyzed. The expression of roundoff noise gain for the proposed structures is obtained.For an N th order allpass digital filter, it yields a roundoff noise gain of 4N if it is realized using anyone of our proposed structures. Therefore, the proposed structure is more suitable for digital system implementation with low complexity and high throughput.4. Implementation of low-cost FIR digital filter on integrated circuit: The subexpression space technology can greatly reduce the number of adders in FIR filter implementations by common subexpression sharing between filter coefficients. The extrapolation technique with residual compensation utilizes the quasi-periodic nature of FIR filter impulse response to reduce the complexity of multiple constants multiplication. Based on the above two kinds of technologies, we realize FIR digital filters on the integrated circuit using hardware description language. In addition, based on the integrated circuit implementation characteristics, high speed and low cost FIR filter realization methods are achieved by improving the hardware structure and will promote the practical application of FIR digital filters.