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Design Of Complex Coefficient FIR Filters With Prescribed Magnitude Error And Phase Error

Posted on:2012-07-10Degree:MasterType:Thesis
Country:ChinaCandidate:D XuFull Text:PDF
GTID:2178330335462667Subject:Control theory and control engineering
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With the development of digital signal processing technology, the complex coefficient FIR filters with asymmetric frequency response are more and more widely used in some applications, such as airborne radar and active sonar systems used to eliminate clutter notch filter, communication channel equalizer, the orthogonal filters of TDM-FDM transmultiplexers and envelope detectors with a Hilbert transformer. Therefore, the design problems of complex FIR filter have attracted more and more attention of researchers.In this thesis, the design problems of complex FIR filter with given magnitude error and phase error will be considered, and the existing design methods of FIR filter with frequency-domain constraints have the following problems:1. Weak methods of constraining error. The three categories of methods of constraining error have been usually used to design FIR filters with constraints in the frequency domain. In the first category, the frequency response error is only constrained. In the second category, constraints are imposed separately and simultaneously on the magnitude error and phase error. In the third category, the magnitude error and group delay error are simultaneously constrained. Because of their existing shortcomings, an improved method is indispensable, so that it is easy to solve the design problems obtained and convenient to control various frequency response errors.2. Non-convex constraints on group delay error. Although many papers have proposed some methods to control group delay error of FIR filter, the basic idea of these methods is directly based on the group delay. Because of non-convex constraints on group delay error, it is necessary to adopt similar methods to translate them into linear constraints or positive definite quadratic constraints, which gets in trouble with dealing them.3. Poor generality of design methods. Many design methods have been proposed to solve design problems of constrained FIR filters, such as linear programming, quadratic programming methods. Some of these methods can only suit the specific type of problems, and some can solve a little more types of problems. With these methods, it is not efficient to solve the design problems of complex FIR filter, especially two-dimensional complex FIR filter.In order to overcome the difficulties encountered in the design of complex FIR filters with given amplitude error and phase error, the following issues are mainly considered in this thesis.1. Application of improved method of constraining error. Because of their respective shortcomings, three traditional methods of constraining error have their own limitations. The literature [8] proposed a method of simultaneously constraining frequency response error and phase error. The proposed method can not only independently control magnitude error and phase error of FIR filter, but also get a convex feasible region, which is convenient to solve the design problems with convex optimization algorithms. This thesis will extend it to the design problems of two-dimensional complex FIR filter, and design examples show the feasibility of the application.2. Generalization of the method of reducing the group delay error. In order to reduce group delay error of low-pass FIR filters at band-edges, the literature [8] proposed a right-side sigmoid upper-bound function of constraining phase error. The results show that this method can effectively reduce the group delay error of filter at band-edges. Firstly, this thesis will extend the above method to one-dimensional design problems of complex FIR filter, and use right-side and double-side sigmoid upper-bound functions to constraining phase error for reducing group delay error at band-edges. Focus of this thesis is to extend this method to two-dimensional complex FIR filter designs, and proposed a two-dimensional sigmoid function to constrain the upper bound of the phase error of the circular filter. Design results demonstrate that the generalized method can efficiently reduce group delay errors of the circular filter at band-edges.3. The application of SDP method. Regarding the design problems of FIR filter with constraints, some of the existing methods can only solve the specific type of problems, and some can solve these problems with a low efficiency. Especially for the design problems of two-dimensional complex FIR filter, solving efficiency with these methods will be lower. The SDP is currently a popular class of mathematical optimization method, which can be used to accurately solve a large number of convex optimization problems. The SDP method adopts sparse matrices and the structures of the diagonal block to store constraint matrices, which boosts efficiency of the algorithm, and more importantly, there are many specialized commercial softwares for solving SDP problems, so the quality of solving problems can be guaranteed. In this paper, the SDP method is used to solve the design problems of complex FIR filter with given amplitude and phase error, and the final design results show efficiency of the SDP method.
Keywords/Search Tags:complex FIR filters, frequency response error, phase error, group delay error, semidefinite programming
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