A New Approach to Time-Frequency Analysis

Summary form only given. Time-frequency analysis is the fundamental methodology in signal processing. It provides a description of signal in the time-frequency plane. Conventionally, in applications of time-frequency analysis, the time domain of a signal is partitioned into intervals at first. Interval by interval, one computes the local frequency spectrum in an interval and then makes signal processing with respect to this local spectrum. The whole procedure goes on while time interval changes. This is the popular, classic approach to time-frequency analysis. To date, the research and applications of time-frequency analysis have been taking this approach. By this approach, signal contents are treated interval by interval locally in time. It neglects the statistical dependency between local frequency spectra in neighboring time intervals. Data compression is an important and successful application of time-frequency analysis. The international standards JPEG(1990), MPEG1(1993), MPEG2(1994), MPEG4(1998), H.264(2003) and JPEG XR(2009) are all good examples. In these systems, image data are encoded in the classic approach to time-frequency analysis. Separately block by block, image data are transformed, quantized and entropy encoded. Another mentionable image coding scheme in classic approach was introduced, where image data are transformed by 8 x 8 DCT. After transform, the 64 coefficients in an 8 x 8 block are treated as a depth-3 tree, without any inter-block regroupment or other operations. Within each block, the coefficients are separately quantized and encoded by the famous EZW method which is popular in wavelet-based image coding. In this paper, we change the way and advocate a new approach to time-frequency analysis. We make signal processing within frequency bands rather than time intervals. We treat signal contents band by band locally in frequency. The new approach gives rise to a good platform to exploit the dependency between local frequency spectra. The ba- - ndwise regrouping technique for new approach is very simple and needs no more computation cost than classic approach. Furthermore, we extend technical design to theoretical constructions. Moreover, we apply the new approach to image data compression. Experiment results show that new approach significantly improves technical performance without increasing computation load. Demo software may be downloaded from website. We expect it may be more useful in other signal processing areas wherever the dependency between local frequency spectra is important for technical performance.