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Contents


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 LTFAT - Quadratic time-frequency distributions

  Jordy van Velthoven, 2014 - 2023.

  Quadratic distributions
    AMBIGUITYFUNCTION   -  Ambiguity function
    WIGNERVILLEDIST     -  Wigner-Ville distribution
    DRIHACZEKDIST       -  Discrete Rihaczek distribution
    QUADTFDIST          -  Generic Quadratic distribution

  Plots
    PLOTQUADTFDIST      - Plot quadratic time-frequency distribution
 
  For help, bug reports, suggestions etc. please visit 
  http://github.com/ltfat/ltfat/issues

   Url: http://ltfat.github.io/doc/quadratic/Contents.html



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 LTFAT - Quadratic time-frequency distributions



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ambiguityfunction


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 -- Function: ambiguityfunction
     AMBIGUITYFUNCTION Ambiguity function
        Usage: A = ambiguityfunction(f);
               A = ambiguityfunction(f,g);
     
        Input parameters:
              f,g    : Input vector(s).
     
        Output parameters:
              A      : ambiguity function
     
        AMBIGUITYFUNCTION(f) computes the (symmetric) ambiguity function of f.
        The ambiguity function is computed as the two-dimensional Fourier transform
        of the Wigner-Ville distribution WIGNERVILLEDIST.
     
        *WARNING**: The quadratic time-frequency distributions are highly
        redundant. For an input vector of length L, the quadratic time-frequency
        distribution will be a L xL matrix.
     *Url*:
     <http://ltfat.github.io/doc/quadratic/ambiguityfunction.html>


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AMBIGUITYFUNCTION Ambiguity function
   Usage: A = ambiguityfunction(f);
    ...



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drihaczekdist


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 -- Function: drihaczekdist
     DRIHACZEKDIST discrete Rihaczek distribution
        Usage r = drihaczekdist(f);
     
     
        DRIHACZEKDIST(f) computes a discrete Rihaczek distribution of vector
        f. The discrete Rihaczek distribution is computed by
     
        where k, l=0,...,L-1 and c is the Fourier transform of f.
     
        *WARNING**: The quadratic time-frequency distributions are highly 
        redundant. For an input vector of length L, the quadratic time-frequency
        distribution will be a L xL matrix. If f is multichannel 
        (LxW matrix), the resulting distributions are stacked along
        the third dimension such that the result is LxL xW cube.
     *Url*: <http://ltfat.github.io/doc/quadratic/drihaczekdist.html>


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DRIHACZEKDIST discrete Rihaczek distribution
   Usage r = drihaczekdist(f);



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plotquadtfdist


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 -- Function: plotquadtfdist
     PLOTQUADTFDIST Plot quadratic time-frequency distribution
        Usage: plotquadtfdist(p);
      
        'plotquadtfdist(p)' plots the quadratic time-frequency distribution 
        on the time-frequency plane. The quadratic time-frequency distribution
        should be a square matrix.
     
        PLOTQUADTFDIST takes the following additional arguments:
     
          'dynrange',r
                   Limit the dynamical range to r by using a colormap in
                   the interval [chigh-r,chigh], where chigh is the highest
                   value in the plot. The default value of [] means to not
                   limit the dynamical range.
     
          'db'     Apply 20*log_{10} to the coefficients. This makes 
                   it possible to see very weak phenomena, but it might show 
                   too much noise. A logarithmic scale is more adapted to 
                   perception of sound. This is the default.
     
          'dbsq'   Apply 10*log_{10} to the coefficients. Same as the
                   'db' option, but assume that the input is already squared.  
     
          'lin'    Show the coefficients on a linear scale. This will
                   display the raw input without any modifications. Only works for
                   real-valued input.
     
          'linsq'  Show the square of the coefficients on a linear scale.
     
          'linabs'  Show the absolute value of the coefficients on a linear scale.
     
          'tc'     Time centring. Move the beginning of the signal to the
                   middle of the plot. 
     
          'clim',clim   Use a colormap ranging from clim(1) to clim(2). These
                        values are passed to imagesc. See the help on imagesc.
     
          'image'       Use imagesc to display the plot. This is the default.
     
          'contour'     Do a contour plot.
               
          'surf'        Do a surf plot.
     
          'colorbar'    Display the colorbar. This is the default.
     
          'nocolorbar'  Do not display the colorbar.
     
          'display'     Display the figure. This is the default.
     
     *Url*: <http://ltfat.github.io/doc/quadratic/plotquadtfdist.html>


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PLOTQUADTFDIST Plot quadratic time-frequency distribution
   Usage: plotquadt...



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quadtfdist


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 -- Function: quadtfdist
     QUADTFDIST Quadratic time-frequency distribution
        Usage p = quadtfdist(f, q);
     
        Input parameters:
              f  : Input vector:w
              q  : Kernel
     
        Output parameters:
              p  : Quadratic time-frequency distribution
      
        For an input vector of length L, the kernel should be a L x L matrix.
        QUADTFDIST(f, q); computes a discrete quadratic time-frequency 
        distribution. 
     
     *Url*: <http://ltfat.github.io/doc/quadratic/quadtfdist.html>


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QUADTFDIST Quadratic time-frequency distribution
   Usage p = quadtfdist(f, q);



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wignervilledist


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 -- Function: wignervilledist
     WIGNERVILLEDIST Wigner-Ville distribution
        Usage: W = wignervilledist(f);
               W = wignervilledist(f, g);
     
        Input parameters:
              f,g      : Input vector(s)
     
        Output parameters:
              w      : Wigner-Ville distribution
     
        WIGNERVILLEDIST(f) computes the Wigner-Ville distribution of the vector f. The
        Wigner-Ville distribution is computed by
     
        where R(n,m) is the instantaneous correlation matrix given by
     
        where m in {-L/2,..., L/2 - 1}, and where z is the analytical representation of
        f, when f is real-valued.
     
        WIGNERVILLEDIST(f,g) computes the cross-Wigner-Ville distribution of f and g.
     
        *WARNING**: The quadratic time-frequency distributions are highly
        redundant. For an input vector of length L, the quadratic time-frequency
        distribution will be a L xL matrix.
     *Url*: <http://ltfat.github.io/doc/quadratic/wignervilledist.html>


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WIGNERVILLEDIST Wigner-Ville distribution
   Usage: W = wignervilledist(f);
 ...





