Joint representations (JR) in signal theory (ST) and hilbertian analysis: A powerful tool for signal analysis

Joint Representations were derived to display signals as an energetic function of time t and frequency γ. These variables are conjugate ones as position ρ and momentum p in Quantum Mechanics (QM). Properties of various JRsare depicted by a measurement system characterized by a weighting function f(n,τ). This function is related to the moments of JR related to modulation properties of signals. Operators defined by hilbertian analysis are associated by various JRsto variables t and γ and functions of them, as in Q.M. Properties of JR are discussed as described by f(n,τ).