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function [f,g]=idgtreal(coef,g,a,M,varargin)
%IDGTREAL Inverse discrete Gabor transform for real-valued signals
% Usage: f=idgtreal(c,g,a,M);
% f=idgtreal(c,g,a,M,Ls);
%
% Input parameters:
% c : Array of coefficients.
% g : Window function.
% a : Length of time shift.
% M : Number of channels.
% Ls : length of signal.
% Output parameters:
% f : Signal.
%
% `idgtreal(c,g,a,M)` computes the Gabor expansion of the input coefficients
% *c* with respect to the real-valued window *g*, time shift *a* and number of
% channels *M*. *c* is assumed to be the positive frequencies of the Gabor
% expansion of a real-valued signal.
%
% It must hold that `size(c,1)==floor(M/2)+1`. Note that since the
% correct number of channels cannot be deduced from the input, `idgtreal`
% takes an additional parameter as opposed to |idgt|.
%
% The window *g* may be a vector of numerical values, a text string or a
% cell array. See the help of |gabwin| for more details.
%
% `idgtreal(c,g,a,M,Ls)` does as above but cuts or extends *f* to length *Ls*.
%
% `[f,g]=idgtreal(...)` additionally outputs the window used in the
% transform. This is usefull if the window was generated from a description
% in a string or cell array.
%
% For perfect reconstruction, the window used must be a dual window of the
% one used to generate the coefficients.
%
% If *g* is a row vector, then the output will also be a row vector. If *c* is
% 3-dimensional, then `idgtreal` will return a matrix consisting of one column
% vector for each of the TF-planes in *c*.
%
% See the help on |idgt| for the precise definition of the inverse Gabor
% transform.
%
% `idgtreal` takes the following flags at the end of the line of input
% arguments:
%
% 'freqinv' Use a frequency-invariant phase. This is the default
% convention described in the help for |dgt|.
%
% 'timeinv' Use a time-invariant phase. This convention is typically
% used in filter bank algorithms.
%
% Examples:
% ---------
%
% The following example demostrates the basic pricinples for getting
% perfect reconstruction (short version):::
%
% f=greasy; % test signal
% a=32; % time shift
% M=64; % frequency shift
% ga={'blackman',128}; % analysis window
%
% [c,Ls]=dgtreal(f,ga,a,M); % analysis
%
% % ... do interesting stuff to c at this point ...
%
% r=idgtreal(c,{'dual',ga},a,M,Ls); % synthesis
%
% norm(f-r) % test
%
% The following example does the same as the previous one, with an
% explicit construction of the analysis and synthesis windows:::
%
% f=greasy; % test signal
% a=32; % time shift
% M=64; % frequency shift
% Ls=length(f); % signal length
%
% % Length of transform to do
% L=dgtlength(Ls,a,M);
%
% % Analysis and synthesis window
% ga=firwin('blackman',128);
% gs=gabdual(ga,a,M,L);
%
% c=dgtreal(f,ga,a,M); % analysis
%
% % ... do interesting stuff to c at this point ...
%
% r=idgtreal(c,gs,a,M,Ls); % synthesis
%
% norm(f-r) % test
%
% See also: idgt, gabwin, gabdual, dwilt
% AUTHOR : Peter L. S��ndergaard.
% TESTING: TEST_DGT
% REFERENCE: OK
% Check input paramameters.
if nargin<4
error('%s: Too few input parameters.',upper(mfilename));
end;
if prod(size(g))==1
error('g must be a vector (you probably forgot to supply the window function as input parameter.)');
end;
% Define initial value for flags and key/value pairs.
definput.keyvals.Ls=[];
definput.keyvals.lt=[0 1];
definput.flags.phase={'freqinv','timeinv'};
[flags,kv,Ls]=ltfatarghelper({'Ls'},definput,varargin);
N=size(coef,2);
W=size(coef,3);
% Make a dummy call to test the input parameters
Lsmallest=dgtlength(1,a,M,kv.lt);
M2=floor(M/2)+1;
if M2~=size(coef,1)
error('Mismatch between the specified number of channels and the size of the input coefficients.');
end;
L=N*a;
if rem(L,Lsmallest)>0
error('%s: Invalid size of coefficient array.',upper(mfilename));
end;
if kv.lt(2)>2
error('Only rectangular or quinqux lattices are supported.');
end;
%% ----- step 3 : Determine the window
[g,info]=gabwin(g,a,M,L,kv.lt,'callfun',upper(mfilename));
if L<info.gl
error('%s: Window is too long.',upper(mfilename));
end;
if ~isreal(g)
error('%s: Window must be real-valued.',upper(mfilename));
end;
% Do the actual computation.
f=comp_idgtreal(coef,g,a,M,kv.lt,flags.do_timeinv);
% Cut or extend f to the correct length, if desired.
if ~isempty(kv.Ls)
f=postpad(f,kv.Ls);
else
kv.Ls=L;
end;
f=comp_sigreshape_post(f,Ls,0,[0; W]);