The representation of multicomponent chirp signals using frequency-shear distribution

We propose a new representation method for multicomponent chirp signals. This representation is based on the 2-D frequency-shear plane. Analytical results for the chirp signals are presented. The analytical results given in the paper have shown that the new frequency-shear distribution provides a more effective tool for analyzing multicomponent chirp signals than the generalized time-frequency distribution. It can suppress the cross terms and clearly locate the signal components onto the frequency-shear plane. In fact, this advantage is caused by introducing a chirplet function that corresponds to the structure of a chirp signal. Similarly, signal representation can be extended to the scale-shear and shift-shear plane using so-called fan bases and chevron bases whose elements scale or translate and shear in the time-frequency plane