Nove klase funkcija za sintezu dvokanalne hibridne banke filtara

Abstract

This PhD discusses the research related to the approximation and implementation of the twochannel hybrid filter banks. Special attention is paid to the analogue part, i.e. analysis part of the hybrid filter banks. Two approximations of the filter bank pair for analysis have been proposed. The first approximation of the transfer function of the low-pass filter is based on the simple adaptation of the orthogonal Jacobi polynomials in order to obtain the Pseudo-Jacobian polynomials. In relation to other known approximations, the Pseudo-Jacobian polynomial one has two prime parameters, which can adjust the characteristics of the filter in wide ranges. This approximation can be successfully applied for the realization of a complementary bank of filters. It is known that recursive double-complementary digital filter banks can be implemented with all-pass filters, and research has shown that double-complementary filter banks can also be realized in the analogue domain. The realization of the proposed filter bank has been done in two steps. In the first step, with the complementary decomposition, the prototype transfer function is obtained by two all-pass filters, while in the second step, by their addition or subtraction, transfer functions of lowpass and highpass filters are obtained. The advantage of such a system is that the same hardware can be used for realization of both low frequency and high frequency transfer functions. Monte Carlo simulation of the realization of a double complementary analog filter pair based on a parallel connection of two analogue all-pass filters showed that all-pass realization is characterized by a small sensitivity of the attenuation characteristics to the component tolerances in the filter pass-band, while the sensitivity in the stop-band is substantially higher compared to the case of a standard cascade realization of the low-pass filter and the high-pass filter. By a suitable selection of the analysis filter bank and the synthesis filter bank, a condition for suppressing the effects arising from the overlapping of the spectrum in banks for analysis and synthesis can be fulfilled. The all-pass complementarity of an analogue filter bank points to the fact that amplitude distortion, which is introduced by the analog bank of the analysis filters, can be completely suppressed, so that the non-linearity of the group delay characteristics is the predominant distortion. In order to achieve a near perfect reconstruction of the signal, a new realization of the group delay corrector was proposed, which makes it possible for the group delay to be constant in a flat sense, i.e. with a number of flatness at the origin. An analysis of the sensitivity has shown that the sensitivity of the correction of the group waveform in the filter pass-band that is proportional to the square of the Q -factor of the pole. In other words, the group delay corrector is very sensitive to the component tolerances.