Covert zero-crossings represent envelope and phase of band-pass signals

The odd-order real zeros of a real-valued signal, s(t), correspond to its conventional or overt zero-crossings. They can be easily determined. But the complex zeros of s(t) are not easy to determine. This suggests the possibility of converting s(t) by using some invertible transformation, into a different signal, whose real zero-crossings determine s(t) completely. This process is known as real-zero conversion. The real zero-crossings of the converted signal are termed covert zero-crossings (cozecs), since they only indirectly determine s(t). In this paper we present a new adaptive algorithm for converting a band-pass signal into a pair of signals whose real zero-crossings essentially determine its envelope and phase. Our algorithm is based on modeling s(t) using pole-zero models in the complex-time (C) plane. Drawing parallels to well known ideas in the area of speech/spectral analysis, we decompose s(t) into its minimum-phase and all-phase components. These components are then represented by their associated zero-crossings.