Frequency transformations of half-band Butterworth filters with filter bank applications

In this paper, we develop a simple procedure for tuning the cut-off frequency of an odd-order IIR Butterworth filter, which is implemented as a parallel connection of two all-pass branches. The start-up filter is a half-band Butterworth filter. The frequency transformations already developed for elliptic filters are adapted for the Butterworth filler case. The constants in all-pass branches are directly computed from the constants of the start-up filter and the desired cut-off frequency. Next, we examine multilevel IIR filter banks composed of Butterworth filter pairs with variable crossover frequency. The discontinuity detection in a non-stationary signal is analyzed using Daubechies, elliptic, and Butterworth half-band filters. Finally, the effects of varying the crossover frequency to discontinuity detection for Butterworth filter banks are examined.