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DESIGN OF IIR FILTERS USING NEW THREE ALLPASS FILTERS STRUCTURE

DESIGN OF IIR FILTERS USING NEW THREE ALLPASS FILTERS STRUCTURE,Alfonso Fernandez-Vazquez,Gordana Jovanovic-Dolecek,Xue Mei Xie

DESIGN OF IIR FILTERS USING NEW THREE ALLPASS FILTERS STRUCTURE  
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We present a new structure for the IIR filter design composed of three allpass filters, i.e., one real-valued and two complex-valued allpass filters. In particular, applying the inverse discrete Fourier transform to the allpass filters, we get three real doubly complemen- tary IIR filters. We also provide the procedure to design a lowpass filter with a desired characteristic using a complex-valued allpass filter with pre-determined characteristics. The proposed structure is used for three different lowpass filter designs, that is, eigenfilter, equiripple, and maximally flat filter design. Closed form equations for the computation of the maximally flat filter coefficients are also provided. The design techniques are illustrated by means of exam- ples. real- and two complex-valued allpass filters. By applying 3-point inverse discrete Fourier transform (IDFT) to the designed allpass filters, we can obtain three transfer functions, which satisfy the dou- bly complementary property. Moreover, the IIR filter implementa- tion is structurally passive. The design problem of lowpass filter is reduced further to design one complex-valued allpass filter with de- sired characteristics. We present three different designs to approxi- mate the desired phase response of the allpass filters, i.e., eigenfilter design, equiripple design, and maximally flat design. Examples are provided in order to illustrate the proposed lowpass filter design. The rest of the paper is organized as follows. The proposed IIR filter based on real- and complex-valued allpass filters is introduced in Section 2. Section 3 presents the design of allpass filters with desired phase responses and complex coefficients based on eigen- filter, equiripple, and maximally flat approaches. Design examples are also given in Section 3.
Published in 2008.
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