Examples of Orthonormal Wavelet Transform Implemented with Iir Filter Pairs

This paper considers the wavelet transform generated by iterating orthonormal power-complementary IIR filter pairs with perfect reconstruction properties. For the implementation of complementary IIR filter pair, the realization structure based on two allpass subfilters in parallel connection is used. The decomposition and reconstruction properties of the example wavelet banks composed of the fifth order IIR filters are examined and compared with those obtained with the seventh order Daubechies 4 (FIR) filter. The experiments have been performed on the portion of an electrocariographic (ECG) signal and on a simple triangle signal. For IIR filter banks, the block processing technique is used to implement anticausal filtering of the synthesis part, and the influence of the finite block length to the reconstruction properties is examined. Wavelet decomposition of the particular test signal with a sudden change in the second derivative is investigated using Daubechies 4 and the fifth order IIR filters. Two-band IIR filter banks with an adjustable crossover frequency have been examined as well. The corresponding wavelet and scaling functions are computed for the various locations of the crossover frequency of the two-band filter pair.