A four-parameter atomic decomposition of chirplets

A new four-parameter atomic decomposition of chirplets is developed for compact representation of signals with chirp components. The four-parameter atom is obtained by scaling the Gaussian function, and then applying the fractional Fourier transform (FRFT), timeshift and frequency-shift operators to the scaled Gaussian. The decomposition is realized by extending the matching pursuit algorithm to four parameters. For this purpose, the four-parameter space is discretized to obtain a dense subset in the Hilbert space. Also, a related time-frequency distribution is developed for clear visualization of the signal components. The decomposition provides a more compact and precise representation of chirp components as compared to the three-parameter ones.