Direktna sinteza digitalnih filtara za podopsežno kodovanje

Abstract

In this PhD thesis two-channel QMF IIR filter banks have been discussed. As a part of this research, direct synthesis of a new IIR filter class, as a lowpass protoype function which satisfies condition for complementary decomposition, has been proposed. Since attenuation characteristic of the new filter class lies in the area between the Butterworth’s and the Elliptic’s attenuation characteristics of the same order, new class has been referred to as Transitional Butter-Elliptic filters. Transfer function of the the lowpass prototype function was separated into two allpass filters by complementary decomposition. Then, lowpass and highpass filters, as power symmetric filter pair, are obtained using those allpass filters. The main advantage of complementary IIR filters based on parallel connection of two allpass filters, is its smaller sensitivity to digital word length change compared to standard filters and low-cost implementation since the same hardware is used for the lowpass and the highpass transfer function. Within the analysis of the new filter class, transfer functions of the odd order with one, two, three and four extremal values of attenuation characteristics in the passband and in the stopband, has been discussed. All types of Transitional filters have been compared with the Butterworth’s and the Elliptic’s filters of the same order. It is shown that in comparison with Butterworth filter, the Transitional filter has better selectivity but lower selectivity than Elliptic filter. However, the proposed new filter class has pure imaginary poles and accuracy in complementary decomposition is at very high level, which the Elliptic filter cannot achieve. Also, the practical realization of the new filter class is easier than for the Elliptic filter since the new class has conjugate-complex zeros on the unit circle and one multiple zero at z = −1. Further, poles and zeros of the Elliptic filter are accumulated near the passband edge and the distance between them decreases as the filter order increases. This requires a very long digital word length for high-order filter realization. The new class filter has approximately equidistant arrangement of poles so it can be realized with shorter digital word length than it is required for the Elliptic filter realization. For Transitional filters class with one extremum of multiplicity L in the passband and in the stopband, closed-form expression for the transfer function coefficients has been obtained. Application of these kind of filters is significant since for sample rate conversion the lowestcomplexity filter is required. With appropriate selection of filters in analysis and synthesis section, the conditions for ii removing the aliasing effects are fulfilled. Magnitude distortions in IIR filter bank can also be completely eliminated and therefore output signal of the QMF bank has only phase distortion. In order to obtain nearly perfect reconstruction of the output signal, the allpass equalizer has been proposed for group delay compensation. Also, effect of the equalizer order on the accuracy of signal reconstruction has been analyzed.