Analysis of Time-Frequency Transient Components Using Phase Chirping Operator

The instantaneous frequency law (IFL) is a very important item when the physical parameters of the corresponding signal have to be evaluated. Radar, sonar, mechanical diagnostic are just three domains where the signal´s non-stationarity imposes the IFL estimation. There are several cases where the IFL is composed by fast variations. Digital phase modulations or signals emitted by electrical switches are typical examples of IFLs having fast transient parts. To deal with such kind of signals, we propose a new method based on the chirping of the phase transitions. Namely, the phase chirping operator (PCO) transforms a fast IFL variation in a chirp component. This chirp contains all the parameters about the initial variation : time, duration, covered bandwidth, etc. Results for some physical data will highlight the benefits of the PCO compared with wavelet transform and Wigner-Ville distribution