Synthesis methods for linear-phase FIR filters with a piecewise-polynomial impulse response
Lehto, Raija (2009)
Tampere University of Technology
Tieto- ja sähkötekniikan tiedekunta - Faculty of Computing and Electrical Engineering
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his thesis concentrates on synthesis methods for linear-phase ﬁnite-impulse response ﬁlters with a piecewise-polynomial impulse response. One of the objectives has been to ﬁnd integer-valued coeﬃcients to efficiently implement ﬁlters of the piecewise-polynomial impulse response approach introduced by Saram¨aki and Mitra. In this method, the impulse response is divided into blocks of equal length and each block is created by a polynomial of a given degree. The arithmetic complexity of these ﬁlters depends on the polynomial degree and the number of blocks. By using integer-valued coefficients it is possible to make the implementation of the subﬁlters, which generates the polynomials, multiplication-free. The main focus has been on ﬁnding computationally-efficient synthesis methods by using a piecewise-polynomial and a piecewise-polynomial-sinusoidal impulse responses to make it possible to implement high-speed, low-power, highly integrated digital signal processing systems. The earlier method by Chu and Burrus has been studied. The overall impulse response of the approach proposed in this thesis consists of the sum of several polynomial-form responses. The arithmetic complexity depends on the polynomial degree and the number of polynomial-form responses. The piecewise-polynomial-sinusoidal approach is a modiﬁcation of the piecewise-polynomial approach. The subresponses are multiplied by a sinusoidal function and an arbitrary number of separate center coefficients is added. Thereby, the arithmetic complexity depends also on the number of complex multipliers and separately generated center coefficients. The ﬁlters proposed in this thesis are optimized by using linear programming methods.
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