On representing signals using only timing information

It is well known that only a special class of bandpass signals, called real-zero (RZ) signals can be uniquely represented (up to a scale factor) by their zero crossings, i.e., the time instants at which the signals change their sign. However, it is possible to invertibly map arbitrary bandpass signals into RZ signals, thereby, implicitly represent the bandpass signal using the mapped RZ signal's zero crossings. This mapping is known as real-zero conversion (RZC). In this paper a class of novel signal-adaptive RZC algorithms is proposed. Specifically, algorithms that are analogs of well-known adaptive filtering methods to convert an arbitrary bandpass signal into other signals, whose zero crossings contain sufficient information to represent the bandpass signal's phase and envelope are presented. Since the proposed zero crossings are not those of the original signal, but only indirectly related to it, they are called hidden or covert zero crossings (CoZeCs). The CoZeCs-based representations are developed first for analytic signals, and then extended to real-valued signals. Finally, the proposed algorithms are used to represent synthetic signals and speech signals processed through an analysis filter bank, and it is shown that they can be reconstructed given the CoZeCs. This signal representation has potential in many speech applications.