We discuss the most common types of weight functions in harmonic analysis and how they occur in time-frequency analysis. As a general rule, submultiplicative weights characterize algebra properties, moderate weights characterize module properties, Gelfand-Raikov-Shilov weights determine spectral invariance, and Beurling-Domar weights guarantee the existence of compactly supported test functions.

The generalized entropies of Rényi inspire new measures for estimating signal information and complexity in the time–frequency plane. When applied to a time–frequency representation (TFR) from Cohen’s class or the affine class, the Rényi entropies conform closely to the notion of complexity that we use when visually inspecting time–frequency images. These measures possess several additional int...

We challenge the perception that we live in a “proper world,” where complex random signals can always be assumed to be proper (also called circularly symmetric). Rather, we stress the fact that the analytic signal constructed from a nonstationary real signal is in general improper, which means that its complementary correlation function is nonzero. We explore the consequences of this finding in...

Holes and clumps, spontaneously formed in the nonlinear development of a single mode driven by a weakly destabilizing kinetic distribution function in a dissipative medium, were expected to persist for an appropriate collisional time scale. However, Fokker-Planck calculations for the nonlinear system abruptly break down in the course of the calculation for some initial conditions. We nd that th...