A new energy distribution on the time-frequency plane

A new time-frequency distribution (TFD) is developed along the line of thinking of the concentration issue of TFDs. A new formulation is given to shed new light on this issue for the short-time Fourier transform (STFT). The new insight is then extended to more general energy density functions and a procedure is developed to construct a complex-valued function which plays a similar role as the STFT does and has a superior concentration limit. The magnitude of this new function is used as the energy density function on the T-F plane. Numerical examples, in certain cases of which the auto terms are preserved while the cross terms are virtually eliminated, justify our intuition