Ljiljana D. Milic

Design of computationally efficient elliptic IIR filters with a reduced number of shift-and-add operations in multipliers

In this paper, a new design method for elliptic IIR filters that provides the implementation of half of the multiplication constants with few shifters and adders is proposed. An IIR filter, when derived by the bilinear transformation from an elliptic minimal Q-factor analog prototype, has its z-plane poles on the circle that is orthogonal to the unit circle and has the center on the real axis of the plane. Due to this property, the center of the circle can be used as a parameter for the representation of a pole, whereas the second parameter is the radius of the pole. It is shown in this paper that the center of the circle is uniquely determined by the frequency for which the filter attenuation is 3 dB. This result is used for the realization based on the parallel connection of two all-pass networks. It is shown that all second-order all-pass sections can be implemented with one common multiplication constant determined by the center of the circle. The design method is presented that, by an appropriate distribution of a margin in the filter performance, predetermines the value of the common constant according to the desired number of shift-and-add operations. This way, half of the multipliers are replaced with a limited number of shifters and adders. Conventional computer programs for IIR elliptic digital filters can be used. The direct approach for the distribution of the z-plane poles among two all-pass functions is developed. The application and efficiency of the proposed design method are demonstrated by examples.

Approximate linear phase multiplierless IIR halfband filter

This paper deals with the real-time multiplierless implementation of halfband IIR filters having approximate linear phase and significantly smaller processing delay than previously reported implementations.

On the Sensitivity of Two-Channel IIR Filter Banks with Variable Crossover Frequency

In this paper, we investigate the sensitivities of the magnitude responses for the two classes of two-channel IIR filter banks. The term class I denotes the IIR filter pair implemented as a parallel connection of two all-pass filters, whereas class II stays for the tapped cascaded interconnection of two identical all-pass filters. A simple tuning scheme that shifts the crossover frequency of the start-up IIR half-band filter pair to the desired location has been introduced recently. In this paper, we concentrate on the effects, which appear when the finite-precision arithmetic is used to implement the tuning formulae. For the two classes of two-channel IIR filter banks, we demonstrate by means of examples the sensitivities of the magnitude frequency characteristics, and show the effects of those sensitivities to the accuracy of the tuning procedure.

Structure of first-order differentiator utilizing FIR and IIR sub-filters

In this paper, we propose a novel approach for constructing the first-order differentiator. It has been shown recently that an efficient FIR wideband differentiator can be synthesized when applying the multirate and frequency-response masking (FRM) techniques. The overall signal processing task is shared between a very low-order differentiator and an FIR half-band filter. The novelty of this paper is the usage of an approximately linear-phase IIR half-band filter based on the parallel connection of all-pass sub-filter and pure delay. The structure of resulting wideband differentiator consists of the approximately-linear phase all-pass sub-filter, two low-order FIR polyphase sub-filters, and the delay element. The proposed system exhibits a significantly smaller overall delay if compared with the corresponding solution based on FIR filters only.

A class of digital filters with variable cut-off based on EMQF filter sections and sharpening method

A new filter class with variable cut-off frequency is designed based on elliptic filter sharpening technique. A higher order IIR filter with a sharp transition band is constructed by using several identical low-order EMQF (elliptic minimal Q-factors) filters and an additional compensating section. The stopband attenuation is achieved by cascading EMQF subfilters, and the compensation section is designed to minimize the overall passband ripple. For the tuning of the cut-off frequency we propose a simple version of the spectral parameter approximation technique. Low-degree approximating polynomials are developed to represent coefficients of the EMQF subfilters and coefficients of the compensating section in terms of the passband cut-off frequency. In the tuning procedure, the new coefficient values are obtained by the polynomial evaluation consisting of several multiplications and additions. The analytical methods are derived for the filter design and for the tuning procedure. Design and implementation of sharp variable filters is illustrated by means of examples.

Design of first–order differentiator utilising FIR and IIR sub–filters

In this paper, we propose a novel approach for constructing the first-order differentiator. It has been shown recently that an efficient Finite Impulse Response (FIR) wideband differentiator can be synthesised when applying the multirate and Frequency-Response Masking (FRM) techniques. The overall signal processing task is shared between a very low- order differentiator and an FIR half-band filter. The novelty of this paper is the usage of an approximately linear-phase IIR half-band filter based on the parallel connection of all-pass sub- filter and pure delay. The structure of resulting wideband differentiator consists of the approximately linear phase all-pass sub-filter, two low-order FIR polyphase sub-filters, and the delay element. The knowledge-based design has been used for the analysis and improvements of the wideband differentiator. The proposed system provides computational savings and exhibits a significantly smaller overall delay if compared with the corresponding solution based on FIR filters only.

Digital filter banks with approximately liner phase

In this paper uniform and nonuniform digital filter banks based on approximately linear phase IIR filters and frequency response masking technique (FRM) are presented. Both solutions are realized as a connection of interpolated half-band approximately linear phase IIR filter as a first stage filter of the FRM design and appropriate number of masking filters. Masking filters are half-band IIR filters with approximately linear phase. Filter banks are compared with linear phase FIR filter banks with similar magnitude responses.