A linear model for the distribution of signals in time and frequency with a historical perspective of conventional time–frequency distributions

We describe a new linear time–frequency model in which the instantaneous value of each signal component is mapped to the curve functionally representing its instantaneous frequency. This transform is linear, uniquely defined by the signal decomposition and satisfies linear marginal-like distribution properties. We further demonstrate that the transform generated surface may be estimated from the short time Fourier transform (STFT) by a concentration process based on the phase of the STFT, differentiated with respect to time. Interference may be identified on the concentrated STFT surface, and the signal with the interference removed may be estimated by applying the linear time marginal to the concentrated STFT surface from which the interference components have been removed.