Abstract: Novel dynamic representations of a complex signal in the time-frequency domain in- cluding: a channelized instantaneous complex frequency (CICF), a complex local group delay (CLGD) and a channelized instantaneous chirp-rate (CICR) are introduced. The proposed approach is based on the use of the gradient of the short-time Fourier transform complex phase. An interpretation of the newly-introduced distributions especially of the CICR is demonstrated by a chirp-rate estimation of mono- and multicomponent FM signals in the time-frequency domain. The paper corresponds to a part of the dissertation.