Wigner-Ville Distribution — Time-Frequency Analysis

Joint time-frequency representation of non-stationary signals
Signal (time domain)
Wigner-Ville Distribution W(t,f)

The WVD is defined as W(t,f) = ∫ x(t+τ/2)·x*(t−τ/2)·e^{−i2πfτ} dτ. For a pure chirp x(t) = e^{iπkt²}, the WVD is a perfectly sharp line in the TF plane — W(t,f) = δ(f−kt). However, when two components are present, cross-terms appear midway between them (a hallmark artifact of the bilinear nature). The STFT and CWT sacrifice resolution for cross-term suppression; the WVD keeps both but reveals the trade-off.