DIGITAL GABOR FILTERS WITH MRA STRUCTURE

Digital Gabor filters are indispensable tools of local time-frequency analysis in signal processing. With strong orientation selectivity, discrete (tight) Gabor frames generated by twodimensional Gabor filters also see their wide applications in image processing and volume data processing. However, owing to the lack of multiscale structures, discrete Gabor frames are less effective than multiresolution analysis (MRA) based wavelet (tight) frames when being used for modeling data composed of local structures with varying sizes. Recently, it was shown that digital Gabor filters do generate MRA-based wavelet tight frames via the unitary extension principle. However, the corresponding window function has to be a constant window, which has poor joint time-frequency resolution. In this paper, we showed that digital Gabor filters with smooth window function can generate MRA-based wavelet biframes. The MRA-based wavelet biframes generated by digital Gabor filters have both the advantages of Gabor systems on local time-frequency analysis and the advantages of wavelet systems on multiscale analysis.