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function g=ref_pchirp(L,n)
%-*- texinfo -*-
%@deftypefn {Function} ref_pchirp
%@verbatim
%PCHIRP Periodic chirp
% Usage: g=pchirp(L,n);
%
% pchirp(L,n) returns a periodic, discrete chirp of length L that
% revolves n times around the time-frequency plane in frequency. n must be
% an integer number.
%
% To get a chirp that revolves around the time-frequency plane in time,
% use :
%
% dft(pchirp(L,N));
%
% The chirp is computed by:
%
% g(l+1) = exp(pi*i*n*(l-ceil(L/2))^2*(L+1)/L) for l=0,...,L-1
%
% The chirp has absolute value 1 everywhere. To get a chirp with unit
% l^2-norm, divide the chirp by sqrt L.
%
% Examples:
% ---------
%
% A spectrogram on a linear scale of an even length chirp:
%
% sgram(pchirp(40,2),'lin');
%
% The DFT of the same chirp, now revolving around in time:
%
% sgram(dft(pchirp(40,2)),'lin');
%
% An odd-length chirp. Notice that the chirp starts at a frequency between
% two sampling points:
%
% sgram(pchirp(41,2),'lin');
%
%
% References:
% H. G. Feichtinger, M. Hazewinkel, N. Kaiblinger, E. Matusiak, and
% M. Neuhauser. Metaplectic operators on c^n. The Quarterly Journal of
% Mathematics, 59(1):15--28, 2008.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_pchirp.html}
%@seealso{dft, expwave}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.2.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% AUTHOR : Peter L. Soendergaard
% TESTING: OK
% REFERENCE: OK
error(nargchk(2,2,nargin));
% Compute normalized chirp
% Old code, has low numerical precision and do not work correctly for odd legths.
%g=(exp((0:L-1).^2/L*pi*i*n)/sqrt(L)).';
% Compute normalized chirp
m = (0:L-1).';
%X = mod(n*(m-ceil(L/2)).^2*(L+1),2*L);
X = mod(n*m.^2*(L+1),2*L);
g = exp(pi*1i*X/L);
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