Reducing aliasing in the Wigner distribution using implicit spline interpolation

The Wigner Distribution (WD) is a bilinear signal transformation possessing several properties that are useful in time-frequency signal analysis. Fast Fourier transform (FFT) techniques have been used to approximate the WD. However, the signal must be sampled at twice the Nyquist rate in order to avoid aliasing errors. This paper deomonstrates that implicit spline interpolation of a continuous time signal or an under sampled discrete time sequence can be used to reduce aliasing errors when approximating the WD. The method is said to be implicit since the interpolated samples are never actually computed. An efficient implicit interpolation algorithm that takes advantage of the special structure and symmetry of the WD is proposed.