Modified Wigner distribution function
Encyclopedia
The Wigner distribution was first proposed for corrections to classical statistical mechanics in 1932 by Eugene Wigner. The Wigner distribution
, or Wigner–Ville distribution (WVD) for analytic signals, also has applications in time frequency analysis. Compared to the short-time Fourier transform
, the Wigner distribution gives better auto term localisation compared to the smeared out STFT. However when applied to a signal with multi frequency components cross terms appear due to its quadratic nature. In 1994 L. Stankovic proposed a novel technique, now mostly referred to as S-method, resulting in the reduction or removal of cross terms.
Wigner distribution function
The Wigner distribution function was first proposed to account for quantum corrections to classical statistical mechanics in 1932 by Eugene Wigner, cf. Wigner quasi-probability distribution....
, or Wigner–Ville distribution (WVD) for analytic signals, also has applications in time frequency analysis. Compared to the short-time Fourier transform
Short-time Fourier transform
The short-time Fourier transform , or alternatively short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time....
, the Wigner distribution gives better auto term localisation compared to the smeared out STFT. However when applied to a signal with multi frequency components cross terms appear due to its quadratic nature. In 1994 L. Stankovic proposed a novel technique, now mostly referred to as S-method, resulting in the reduction or removal of cross terms.
Mathematical definition
The concept of the S-method is a combination between the STFT and the Pseudo Wigner Distribution (PWD), the windowed version of the WD.- Wigner distribution
- Pseudo-Wigner distribution
- S-method
is a windowing function in the frequency domain resulting in the cross term removal.
See also
- Time-frequency representationTime-frequency representationA time–frequency representation is a view of a signal represented over both time and frequency. Time–frequency analysis means analysis into the time–frequency domain provided by a TFR...
- short-time Fourier transformShort-time Fourier transformThe short-time Fourier transform , or alternatively short-term Fourier transform, is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time....
- Gabor transformGabor transformThe Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time...
- Wigner distribution functionWigner distribution functionThe Wigner distribution function was first proposed to account for quantum corrections to classical statistical mechanics in 1932 by Eugene Wigner, cf. Wigner quasi-probability distribution....