Signal analysis/synthesis based on zeros in holomorphic time-frequency plane

In this paper, we propose a new framework of the time-frequency analysis based on zeros, which are fundamental and important features in the signal processing. Firstly, we derive a generalized form of specific filter banks, on which logarithmic differentials of subband signals are holomorphic. Next, we prove that, in decomposing an input signal into subband signals by using such filter banks, the input signal is completely represented by locations of zeros on the time-frequency plane except a constant multiple. Finally, we show experimental results of signal analysis/synthesis based on zeros.