Optimization Structure For Finite Word Length FIR Digital Filters

Digital signal processing(DSP)technology is one of the important foundations for the development of modern information technology.Digital filter is the core component of digital system used for signal filtering.Due to the affection of finite word length(FWL)quantization,the actual filtering performance of digital filters implemented on finite precision devices often falls short of the expected design requirements.The optimization design and implementation of digital filters with finite word length has always been an important topic in the research areas of digital signal processing.The finite impulse response(FIR)filter is widely used in mobile communications,video and image processing since their strict linear phase characteristics.At present,most of the research on the optimal structure of finite word length focuses on the infinite impulse response(IIR)filter.Based on the state space theory,this thesis discusses the sensitivity of FIR filters to finite precision errors from the structural design,to enhance the ability of FIR filter to resist finite word length effects.The main contents of the research include as follows:1.Aiming at the problem of pole and zero deviation of filters which caused by the finite word length effects,the thesis studies the sensitivity of pole and zero for FIR digital filters to coefficient errors based on the state-space model.First,since the system matrix in state-space model of the FIR filter was defective,the pole sensitivity cannot be analyzed using the linear independence of eigenvectors of nondefective matrix.In this thesis,a set of linearly independent generalized eigenvectors and their adjoint vectors of the system matrix are introduced,and the pole sensitivity measure for FIR filters is analyzed and formulated based on the method of perturbation analysis.Then,by finding optimal transformation matrices according to the similarity transformation theory,the optimal realizations with respect to pole-zero sensitivity for FIR filters were proposed.Theoretical analysis and simulation results show that the poles of a FIR filter are more sensitive to coefficient errors,the pole and zero sensitivity of filter is depend upon the implementation structure,and the proposed optimal realizations can reduce the sensitivity.2.Aiming at the problem of the distortion of frequency response curve when a FIR filter implemented with finite precision,this thesis introduces the incremental differential delta operator method,which has good numerical characteristics in high-speed sampling,into the filter structure design,and proposes optimization structures of sensitivity for FIR filters based on the delta operator.By means of the state space analysis,the sensitivity of the transfer function with respect to structural parameters is measured,and the corresponding sensitivity expressions are formulated.Theoretical analysis and simulation results show that the proposed optimal structures in delta operator have lower sensitivity than the structure in traditional shift z operator,the value of sensitivity decreases with increasing sampling frequency,and its frequency response characteristics are more stable under the finite word length constraints.