On The Design Of Robust Low Complexity Digital Filter Structures

The modern science and technology has brought about great advances in human soci-ety, and also puts forward increasing demands for energy sources. According to the change of international situation, the country proposed the strategic planning for new energy and encouraged the community to explore the application fields of new energy. It should be pointed out that research on new energy is one of the most important steps to solve the energy crisis, however, energy-saving is a principal method for dealing with the energy cri-sis. Accompanying with the rapid development of information technology, digital signal processing (DSP) technology has sped. As the core of DSP, digital filters have lots of su-periorities such as high precision, great flexibility and being easy to be integrated such that they are found applications almost everywhere. As a consequence of that, the amount of power consumed by these digital device is huge. Therefore, how to design a filter struc-ture with high performance and low power consumption has been an important topic in this areas.Infinite precision design theory for digital filters has been mature relatively and widely used. Theoretically, a well-designed digital filter can be implemented with many different structures. These structures are totally equivalent in infinite precision implementation as they represent the same transfer function. For real-time applications, digital filters have to be realized on a finite word length (FWL) physical components or platform such as a full-custom ASIC and the performance of the actual transfer function may deviate from the ideal one. It can be shown that the performance of FWL implemented filter depends on the realization structure and different realization structure may yield very different perfor-mance. Hence, FWL must be considered in the process of design as well as implementation of the digital filter. The theory of system structures developed recently provides an effec-tive way to solve this problem and has attracted a lot of attention. In this thesis, in order to enhance the performance of digital systems we focus on investigating the theory and ap-proach to design robust and sparse system structures. The main contributions in this thesis are summarized as follows.1. A sparse orthogonal filter structure:Noting that the state space realizations are not unique, we carry out some in-depth study of a special input balance realization. Based on the theory of matrix decomposition, a sparse orthogonal structure has been derived by decomposing the transition matrix. Compared with the optimal state space realizations of an Nth order digital filter, the proposed structure requires only4N-1multiplications instead of (N+1)2for computing one output sample, which can save resource and reduce the power consumption greatly. Experimental results have justified the robustness of the proposed structure against the FWL effect in terms of parameter sensitivity and roundoff noise gain.2. Input-balanced state space realizations:Compared with direct-form structures, cascade-based structures have less influence on FWL effects from the devices. An efficient way used in practice for implementation of digital filters is to cascade a high order filter into a series of2nd order sub-filters and then to implement each sub-filter with an optimal structure. Based on a new parametrization of the input-balanced realizations a novel struc-ture is proposed for implementation of2nd order digital filters, which can be implemented much efficiently using the COordinate Rotation DIgital Computer (CORDIC) techniques. Moreover, the expression of roundoff noise gain for the normalized lattice structure is de-rived, based on which it is shown that an all-pass system, when implemented using the normalized lattice structure, yields a very low roundoff noise gain. Hence, if an Nth order system is decomposed into two all-pass subsystems in parallel and each all-pass subsystem is realized using the normalized lattice structure, this structure may reveal excellent FWL properties. Such an all-pass system realized using the normalized lattice structure and the2nd order state space realization actually are special input-balanced realizations.3. An effective lattice filter structure:The structure parameters of the traditional lattice structures are filter dependent and hence have no extra degrees of freedom to opti-mize a certain measure/criterion, such as roundoff noise gain and sensitivity measure. In order to develop a structure with degrees of freedom, a novel lattice filter structure is pro-posed by combining the tapped numerator and injected numerator lattices. The remarkable advantage of this structure is that the injector coefficients can be optimized for a FWL per- formance while the tapped coefficients are used to synthesize the transfer function of the filters. The optimized structure, like the direct-form structures, has only2N+1multipliers, and yields very low parameter sensitivity, which is of important contribution to the lattice filter theory.4. A set of lattice filter structures:It is shown that the five elementary lattices have different characteristics even their expressions of transfer function are similar. Actually, one elementary lattice can be distinguished from the others by their own scaling factors and such scaling factors may change the performance of the whole filter. Based on this observa-tion, a novel lattice-based structure is proposed with each stage taking different elementary lattices. By introducing another degree of freedom called elementary lattice combinations, a set of filter structures is established. The optimal structure problem has been formulated in terms of minimizing the signal power ratio. With the increasing of number of free pa-rameters, exhaustive search is unsuitable for solving the involved optimization problem. An efficient gray-based genetic algorithm (GA) is proposed to attack the optimal structure problem, which effectively solves the contradiction between performance and efficiency in the filter structure design problems.