Time-frequency phase space — quantum quasi-probability in signal form
Signal x(t)
Wigner-Ville W(t,f)
Wigner-Ville distribution: W(t,f) = ∫ x(t+τ/2)·x*(t−τ/2)·e−i2πfτ dτ. It is the unique bilinear time-frequency distribution satisfying both marginals — integrating over f gives |x(t)|², integrating over t gives |X(f)|². Unlike spectrograms, WVD has no window-blurring, but produces cross terms (interference fringes) between signal components — visible as oscillating negative regions between two simultaneous tones. These cross terms are a direct analog of quantum phase-space interference in the Wigner function.