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 lowpa...ss 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.
