Optimal Design Of High-Performance Fir Filters For Wireless Communication

Digital filter plays an important role in the application of digital signal processing, and also serves as a key part of digital transmitter and receiver. With fast development of wireless communication technology, the requirements for highly performance digital filters have been urgent. Generally, the linear phase response property is preferred in the design of matching filters for wireless communication system. Thus, this thesis focuses on the linear phase FIR filters.Firstly, this thesis studied the specification trade-off relationship of linear phase FIR filters. The concept of inter-symbol interference (ISI) in frequency domain is proposed. So are the corresponding constrained op-timization methods for linear phase matching filter. Constructed a multi-objective optimization (MOP) model of passband\stopband ripple, passband\stopband energy, tails energy and ISI in frequency domain based on the MOP theory. Exploited mathematical programming methods to generate the Pareto solution and showed the Pareto boundaries in the form of figures and tables. This work enriched the meaning of Losada’s triangle met-aphor.Secondly, this thesis improved the peak-error-gradient (PEG) method. The conventional PEG method ex-ploited the simple fixed step size strategy, which might fail to converge if the step size is too large while re-quire lots of iterations if the step size is too small. Thus, a dynamic step size strategy aiming at accelerating the algorithm via generating larger step size in the earlier stage and reducing the convergent error via generating smaller step size in the later stage. The effectiveness of this improved strategy is demonstrated by Monte Carlo simulation that generates lots of initial values randomly. Furthermore, a proof based on subgradient theory is given, where the relationships between the upper bounds of convergent error and the number of iteration are also pointed out. Some other optimization models are constructed which extended the application of PEG method and confirmed the specification trade-off relationship discussed in chapter three.Finally, this thesis studied the particle swarm algorithm optimization scheme for frequency sampling method. The frequency sampling method is analyzed and the equivalence of samples in frequency domain and the coefficients in time domain is pointed out. Analyzed the deficiencies of existing frequency sampling methods. And a strategy that adjusting all samples is proposed. The passband (stopband) ripple is a relatively tight upper bound of maximal range of samples in passband (stopband). Both the passband ripple and stopband ripple can be estimated according to the filter length estimation formulae. This pleasing property can applied to narrow the ranges of some samples reasonably which make it possible to shrink the search space. And experi-mental results showed that this strategy is help to accelerate the evolutionary rate and improve the filters’ per-formance.