Time-Frequency Characterization using Instantaneous Moment Concept : Theory and Applications

The instantaneous frequency law (IFL) is a very important element when the physical parameters of the corresponding signal have to be evaluated. Blind equalisation, modulation recognition and mechanical diagnostic are just three domains where the signal´s non-stationarity imposes the IFL estimation. Generally, an IFL is composed by slowly varying time-frequency structures separated by fast transitions which could be considered as phase discontinuities. Digital phase modulations or signals propagated trough a multi-path channel are typical examples of IFLs having fast transient parts. The common methods employed for these operations are wavelet transform and Cohen´s class time-frequency representation, respectively. In this paper we propose an alternative based on the instantaneous moments. By an appropriate choice of the moment order and lag it is possible to accurately estimate both transient and slowly time-frequency parts. While this method uses one dimensional data and, thanks to its recursive structure, it is well suited for real time applications. Therefore, its real-time implementation on TMS320C6x structure is described. On the other hand, few examples on realistic data shows the practical interest for this method