Three-band biorthogonal interpolating complex wavelets with stopband suppression via lifting scheme

Abstract

Wavelet research has primarily focused on real-valued wavelet bases. However, the complex filterbanks provide much convenience for complex signal processing. For example, in radar and sonar signal processing, the complex signals from the I/Q receiver can be efficiently processed with complex filterbanks rather than real filterbanks. Specifically, the positive and negative Doppler frequencies imply different physical content in the moving target detector (MTD) and moving target identification (MTI); therefore, it is significant to design complex multiband filterbanks that can partition positive and negative frequencies into different subbands. We design two novel families of three-band biorthogonal interpolating complex filterbanks and wavelets by using the three-band lifting scheme. Unlike the traditional three-band filterbanks, the novel complex filterbank is composed of three channels, including the lowpass channel, the positive highpass channel whose passband distributes in the positive frequency region, and the negative highpass channel in the negative frequency region. Such a filterbank/wavelet naturally provides the ability to extract positive frequency components and negative frequency components from complex signals. Moreover, a novel set of design constraints are introduced to manipulate the stopband characteristic of highpass filters and are referred to as stopband suppression, which strengthens the traditional constraints of vanishing moments. Finally, a numerical method is given to further lower stopband sidelobes.