S-method based on modified group delay for time-frequency analysis

A noise robust time-frequency representation based on the S-method (SM) and modified group delay (MGD) (S-MGD) is proposed in this article. The SM is free from cross-terms as it is the sum of individual Wigner distributions of different signal components and provides high-energy concentration both in time and frequency. The MGD reduces the Gibbs ripple and spurious spectral peaks because of noise, without using any frequency smoothing, and thus maintains the best frequency resolution as that of rectangular window. Hence,a combination of SM and MGD provides the desirable features of both the methods. The proposed method is tested for different signals like time varying random process, frequency shift keying, synthesized car engine sound/pressure signals using a solo combustion and a real-time echolocation pulse emitted by a big brown bat (Eptesicus fuscus) which indicate that the new S-MGD has improved noise immunity and frequency resolution compared to the method that uses frequency smoothing to suppress noise and Gibbs effects.