Cross Psi(B)-energy operator-based signal detection

In this paper, two methods for signal detection and time-delay estimation based on the cross Psi(B)-energy operator are proposed. These methods are well suited for mono-component AM-FM signals. The Psi(B) energy operator measures how much one signal is present in another one. The peak of the Psi(B) operator corresponds to the maximum of interaction between the two signals. Compared to the cross-correlation function, the Psi(B) operator includes temporal information and relative changes of the signal which are reflected in its first and second derivatives. The discrete version of the continuous-time form of the Psi(B) operator, which is used in its implementation, is presented. The methods are illustrated on synthetic and real signals and the results compared to those of the matched filter and the cross correlation. The real signals correspond to impulse responses of buried objects obtained by active sonar in iso-speed single path environments.