Function: filterbankreassign
FILTERBANKREASSIGN  Reassign filterbank spectrogram
  Usage:  sr = filterbankreassign(s,tgrad,fgrad,a,cfreq);
          sr = filterbankreassign(s,tgrad,fgrad,a,g);
          [sr,repos,Lc] = filterbankreassign(...);

  Input parameters:
     s     : Spectrogram to be reassigned.
     tgrad : Instantaneous frequency relative to original position.
     fgrad : Group delay relative to original position.
     a     : Vector of time steps.
     cfreq : Vector of relative center frequencies in ]-1,1].
     g     : Set of filters.
  Output parameters:
     sr    : Reassigned filterbank spectrogram.
     repos : Reassigned positions.
     Lc    : Subband lengths.

  FILTERBANKREASSIGN(s,tgrad,fgrad,a,cfreq) will reassign the values of
  the filterbank spectrogram s using the group delay fgrad and
  instantaneous frequency tgrad. The time-frequency sampling
  pattern is determined from the time steps a and the center
  frequencies cfreq.

  FILTERBANKREASSIGN(s,tgrad,fgrad,a,g) will do the same thing except
  the center frequencies are estimated from a set of filters g.

  [sr,repos,Lc]=FILTERBANKREASSIGN(...) does the same thing, but in addition
  returns a vector of subband lengths Lc (Lc = cellfun(@numel,s))
  and cell array repos with sum(Lc) elements. Each element corresponds
  to a single coefficient obtained by cell2mat(sr) and it is a vector
  of indices identifying coefficients from cell2mat(s) assigned to
  the particular time-frequency position.

  The arguments s, tgrad and fgrad must be cell-arrays of vectors
  of the same lengths. Arguments a and cfreq or g must have the
  same number of elements as the cell arrays with coefficients.

  Examples:
  ---------

  This example shows how to reassign a ERB filterbank spectrogram:

    % Genrate 3 chirps 1 second long
    L = 44100; fs = 44100; l = 0:L-1;

    f = sin(2*pi*(l/35+(l/300).^2)) + ...
        sin(2*pi*(l/10+(l/300).^2)) + ...
        sin(2*pi*(l/5-(l/450).^2));
    f = 0.7*f';

    % Create ERB filterbank
    [g,a,fc]=erbfilters(fs,L,'fractional','spacing',1/12,'warped');

    % Compute phase gradient
    [tgrad,fgrad,cs,c]=filterbankphasegrad(f,g,a);
    % Do the reassignment
    sr=filterbankreassign(cs,tgrad,fgrad,a,cent_freqs(fs,fc));
    figure(1); subplot(211);
    plotfilterbank(cs,a,fc,fs,60);
    title('ERBlet spectrogram of 3 chirps');
    subplot(212);
    plotfilterbank(sr,a,fc,fs,60);
    title('Reassigned ERBlet spectrogram of 3 chirps');


  References:
    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/filterbankreassign.html

See also: filterbankphasegrad, gabreassign.

Package: ltfat