Miroslav D. Lutovac

Design of multiplierless elliptic IIR filters with a small quantization error

We present a new technique for the design of multiplierless IIR elliptic filters. The multiplierless filter has all multiplication constants implemented with a small number of shifters and adders. The proposed technique is based on sensitivity analysis. An analytical expression for amplitude response sensitivity is derived for the filter structures consisting of two allpass subfilters in parallel. It is shown that the amplitude response sensitivity to some constant x can be expressed as a product of the filter reflectance function and the phase sensitivity of the allpass section that implements the constant. The closed-form expressions for the phase sensitivities of the first- and second-order allpass sections are also developed. It is shown in the paper that the (n+1)/2 most sensitive constants can be directly controlled by the transfer function parameters if the transfer function is derived by the bilinear transformation from an elliptic minimal Q-factors (EMQF) analog prototype. This way, (n+1)/2 multiplication constants can be implemented without quantization, leaving the filter characteristic strictly elliptic. This is achieved for a class of low-noise allpass sections and for the wave lattice digital filter as well. The quantization of the remaining (n-1)/2 less-sensitive constants is performed using the phase-tolerance scheme and phase-sensitivity functions. The proposed design technique is straight-forward and, consequently, very fast. The application is demonstrated on the examples of narrowband, wideband, and halfband filters.

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.

Symbolic analysis and design of control systems using Mathematica

Contemporary computer tools can generate a tremendous amount of numerical data so the user might easily lose insight into the phenomenon being investigated. Those who use powerful computer algebra systems must thoroughly understand the assumptions that underlie the software. In this paper, the role and importance of symbolic computation in control engineering and signal processing is exemplified. Real-life application examples are presented in which systems are symbolically solved and simulated with Mathematica. We introduce an original approach to algorithm development, system design and symbolic processing that successfully overcomes some problems encountered in the traditional approach. Benefits of symbolic methods and the role of computer algebra systems are highlighted from the viewpoint of both academia and industry.

A new improvement to the Powell and Chau linear phase IIR filters

An improvement to the realization of the linear-phase IIR filters is described. It is based on the rearrangement of the numerator polynomials of the IIR filter functions that are used in the real-time realizations proposed in literature. The new realization has better total harmonic distortion when a sine input is used, and it has smaller phase and group delay errors due to finite section length.

Advanced filter design

Classical filter design techniques return only one design from an infinite collection of alternative designs, or fail to design filters when solutions exist. These classical techniques hide a wealth of alternative filter designs that are more robust when implemented in analog circuits, digital hardware, and embedded software. We present (1) case studies of optimal analog and digital IIR filters that cannot be designed with classical techniques, and (2) the formal, mathematical framework that underlies their solutions. We have automated the advanced filter design techniques in software.

Reducing the number of multipliers in the parallel realization of half-band elliptic IIR filters

It is shown in this correspondence that a halfband IIR filter with the poles on the imaginary axis can be derived by the bilinear transformation of an elliptic minimal Q-factors analog prototype. For an odd degree transfer function, the residues at the poles are real or imaginary. Consequently, in the parallel realization, the number of multipliers can be reduced by half.

High speed IIR filters for QMF banks

In this paper, we show that using allpass IIR subfilters and half-band FIR optimal filters from the minimal phase solution it is possible to design a filter which exhibits simultaneously very low passband attenuation, large stopband attenuation, narrow transition region and low arithmetic complexity, and thus high maximal sample frequency. We introduce the closed form relations for the design of fast IIR filters for interpolation, decimation, and QMF banks with perfect magnitude reconstruction. The design is based on the third-order half-band IIR filters and the fifth-order non minimum-phase optimal FIR filters.

Automated knowledge–based filter synthesis using modified Legendre approximation and optimisation of summed sensitivity

The paper presents the automated design of active RC and programmable filters. The approximating function is derived using Legendre orthogonal polynomial with the appropriate weights and usage of two Legendre multiplication factors at the origin and the pass–band edge frequency. Detailed analysis is done for the frequency response and sensitivity analysis of active RC filters. Optimisation is performed using symbolic manipulation of expressions inputted into computer algebra system and numeric solvers. The code is in the form of template notebook, and the user should specify the minimal number of numeric values, such as the number of second–order filter sections, the pass–band edge frequency, the reflection coefficient, and the preferred values of component values.

A solution for efficient reduction of intersymbol interference in digital microwave radio

In this paper we describe one simple solution for improving the performance of digital microwave radio system under conditions of intersymbol interference. Presented structure of ¿blind¿ adaptive equalizer is characterised with low complexity, suitable for implementation on FPGA, and can be used for efficient reduction of intersymbol interference in order to satisfy demands defined by standardization institutions.