Function: filterbankphasegrad
FILTERBANKPHASEGRAD   Phase gradient of a filterbank representation
  Usage:  [tgrad,fgrad,s,c] = filterbankphasegrad(f,g,a,L,minlvl);
          [tgrad,fgrad,s,c] = filterbankphasegrad(f,g,a,L);
          [tgrad,fgrad,s,c] = filterbankphasegrad(f,g,a,minlvl);
          [tgrad,fgrad,s,c] = filterbankphasegrad(f,g,a);
          [tgrad,fgrad,s] = filterbankphasegrad(...)
          [tgrad,fgrad]  = filterbankphasegrad(...)

  Input parameters:
     f     : Signal to be analyzed.
     g     : Cell array of filters
     a     : Vector of time steps.
     L     : Signal length (optional).
     minlvl: Regularization parameter (optional, required < 1).
  Output parameters:
     tgrad : Instantaneous frequency relative to original position.
     fgrad : The negative of the local group delay. 
     cs    : Filterbank spectrogram.
     c     : Filterbank coefficients.

  [tgrad,fgrad,s,c] = FILTERBANKPHASEGRAD(f,g,a,L) computes the 
  relative instantaneous frequency tgrad and the negative of the group
  delay fgrad of the filterbank spectrogram s obtained from the 
  signal f and filterbank parameters g and a. 
  Both tgrad and fgrad are specified relative to the original 
  coefficient position entirely similar to GABPHASEGRAD.
  fgrad is given in samples, while tgrad is given in normalised
  frequencies such that the absolute frequencies are in the range of ]-1,1]. 

  This routine uses the equivalence of the filterbank coefficients in 
  each channel with coefficients obtained from an STFT obtained with a
  certain window (possibly different for every channel). As a consequence
  of this equivalence, the formulas derived in the reference apply. 


  References:
    F. Auger and P. Flandrin. Improving the readability of time-frequency
    and time-scale representations by the reassignment method. IEEE Trans.
    Signal Process., 43(5):1068--1089, 1995.
    
    N. Holighaus, Z. Průša, and P. L. Soendergaard. Reassignment and
    synchrosqueezing for general time-frequency filter banks, subsampling
    and processing. Signal Processing, 125:1--8, 2016. [1]http ]
    
    References
    
    1. http://www.sciencedirect.com/science/article/pii/S0165168416000141
    

Url: http://ltfat.github.io/doc/filterbank/filterbankphasegrad.html

See also: gabphasegrad.

Package: ltfat