Are quadratic time-frequency representations really necessary?

Quadratic time frequency representations (TFRs), such as the Wigner-Ville function (WVF), have been promoted as alternatives to linear TFRs, such as the short-time Fourier transform (STFT), due to their apparent higher resolution time-vs-frequency feature localization capabilities. However, this is achieved at the price of cross term artifacts and, as this paper indicates, the improvement in time-frequency resolution is only at best a factor of two. Two new two-dimensional (2-D) functions, the windowed data function (WDF) and the complex WDF transform (CWT), are introduced which permit high-resolution 2-D spectral analysis techniques to be applied to create new linear TFRs which have no cross term artifacts while achieving higher resolution than quadratic TFRs. This raises the question as to the need for quadratic TFR techniques.