Design of Quadrature Mirror Hilbert Transformers Using Even-Order Elliptic IIR Filters

Signals in a two-channel quadrature mirror filter bank are decomposed into low and high frequency components. Similarly, analytic signals can be extracted from the original signal with only positive or negative frequency contents. Multirate systems based on this idea are called quadrature mirror Hilbert transformers. Just like the case of quadrature mirror filter banks, the FIR and IIR designs are free from phase and amplitude distortion, respectively. However, the previous researches on quadrature mirror Hilbert transformers do not include the case of even-order IIR filters. In this paper, we investigate the design and realization of quadrature mirror Hilbert transformers for even-order elliptic IIR filters. It is found that the distortion transfer function can not eliminate the amplitude distortion completely. Nevertheless, a design example is given to show that the magnitude of the distortion is close to an allpass filter and exhibits the property of a practical Hilbert transformer. Keywords—Quadrature mirror filter bank, complex half-band filter, Hilbert transformer, elliptic IIR filter.