Highly concentrated time-frequency distributions: pseudo quantum signal representation

Distributions that are highly concentrated in the time-frequency plane are presented. Since the idea for these distributions originated from the Wigner representation in the quantum mechanics, a review of this representation is done in the first part of the paper. Abstracting the physical sense of the quantum mechanics representation, we defined the “pseudo quantum” signal representation. On the basis of a signal, the “pseudo wave function” with the corresponding “pseudo particle” having the “pseudo momentum” } = hf! is generated. By varying the value of hf , one is in a position to influence the concentration of the “pseudo quantum” (time-“pseudo momentum”) signal’s presentation while keeping its most important timefrequency properties invariant. From this reflection, an efficient distribution for the time-frequency (time-“pseudo momentum”) signal analysis is obtained. This distribution produces as high a concentration in the time-frequency (time-“pseudo momentum”) plane as the L-Wigner distribution; however, it may satisfy the marginal properties. The theory is illustrated with examples.