A Class of Time-Frequency Product Optimized Biorthogonal Wavelet Filter Banks
The analysis of non-stationary signals involves a trade-off in the sense that one has to sacrifice time localization in order to achieve better frequency localization and vice versa. If the authors assume that the function is normalized, the uncertainty principle states that the product of the time-spread (defined in the variance-sense) and frequency spread is bounded below by 0.25. The design of filter banks has generally been developed keeping in mind criteria such as energy compaction, non-aliasing energy ratio, coding gain, etc. However time-frequency localization is a fundamental limitation in signal processing in one dimension as well as in higher dimensions, and literature on time-frequency localization optimized filter bank design has been relatively sparse.