www.gusucode.com > 线性时频分析工具箱 - ltfat-1.0.1源码程序 > 线性时频分析工具箱 - LTFAT\fourier\firwin.m
function [g,info]=firwin(name,M,varargin);
%FIRWIN FIR window
% Usage: g=firwin(name,M);
% g=firwin(name,M,...);
%
% FIRWIN(name,M) will return a FIR window of length M of type name.
%
% All windows are symmetric, they are zero delay and zero phase
% filters. They can be used for Wilson bases, except when noted otherwise.
%
% If a window g forms a "partition of unity" (PU) it means specifically
% that
%
% g+fftshift(g)==ones(L,1);
%
% A perfect PU can only be formed if the window length is even, but
% some windows may work for odd lengths anyway.
%
% If a window is the square root of a window that forms a PU, the window
% will generate a tight Gabor frame / orthonormal Wilson/WMDCT basis if
% the number of channels is less than M.
%
% The windows available are:
%
% hann - von Hann window. Forms a PU.
%
% sine - Sine window. This is the square root of the Hanning
% window. Aliases: 'cosine', 'sqrthann'
%
% square - (Almost) rectangular window. Forms a PU. Alias: 'rect'
%
% sqrtsquare - Square root of the square window.
%
% tria - (Almost) triangular window. Forms a PU. Alias: 'bartlett'
%
% sqrttria - Square root of the triangular window.
%
% hamming - Hamming window. Forms a PU that sums to 1.08 instead
% of 1.0 as usual. This window should not be used for
% a Wilson basis, as a reconstruction window cannot be
% found by WILDUAL.
%
% blackman - Blackman window
%
% nuttall - Nuttall window
%
% itersine - Iterated sine window. Generates an orthonormal
% Wilson/WMDCT basis. This window is described in
% Wesfreid and Wickerhauser (1993) and is used in the
% ogg sound codec. Alias: 'ogg'
%
% FIRWIN understands the following flags at the end of the list of input
% parameters:
%
% 'wp' - Output is whole point even. This is the default.
%
% 'hp' - Output is half point even, as most Matlab filter
% routines.
%
% 'taper',t - Extend the window by a flat section in the middle. The
% argument t is the ratio of the rising and falling
% parts as compared to the total length of the
% window. The default value of 1 means no
% tapering. Accepted values lie in the range from 0 to 1.
%
% Additionally, FIRWIN accepts flags to normalize the output. Please see the
% help of NORMALIZE. Default is to use 'peak' normalization.
%
% See also: pgauss, pbspline, firkaiser, normalize
%
% References:
% A. V. Oppenheim and R. W. Schafer. Discrete-time signal processing.
% Prentice Hall, Englewood Cliffs, NJ, 1989.
%
% A. Nuttall. Some windows with very good sidelobe behavior. IEEE Trans.
% Acoust. Speech Signal Process., 29(1):84-91, 1981.
%
% F. Harris. On the use of windows for harmonic analysis with the
% discrete Fourier transform. Proceedings of the IEEE, 66(1):51 - 83, jan
% 1978.
%
% E. Wesfreid and M. Wickerhauser. Adapted local trigonometric transforms
% and speech processing. IEEE Trans. Signal Process., 41(12):3596-3600,
% 1993.
% Copyright (C) 2005-2011 Peter L. Soendergaard.
% This file is part of LTFAT version 1.0.1
% 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 Soendergaard.
% REFERENCE: NA
if nargin<2
error('Too few input parameters.');
end;
% Always set to this
info.isfir=1;
% Default values, may be overwritten later in the code
info.ispu=0;
info.issqpu=0;
name=lower(name);
% Define initial value for flags and key/value pairs.
definput.import={'normalize'};
definput.importdefaults={'null'};
definput.flags.centering={'wp','hp'};
%definput.flags.delay={'nodelay','delay','causal'};
definput.keyvals.taper=1;
%definput.keyvals.delay=0;
[flags,keyvals]=ltfatarghelper({},definput,varargin);
if flags.do_wp
cent=0;
else
cent=0.5;
end;
if M==0
g=[];
return;
end;
% Deal with tapering
if keyvals.taper<1
if keyvals.taper==0
% Window is only tapering, do this and bail out, because subsequent
% code may fail.
g=ones(M,1);
return;
end;
% Modify M to fit with tapering
Morig=M;
M=round(M*keyvals.taper);
Mtaper=Morig-M;
p1=round(Mtaper/2);
p2=Mtaper-p1;
% Switch centering if necessary
if cent==0 && p1~=p2
cent=0.5;
end;
if cent==0.5 && p1~=p2
cent=1;
end;
end;
% This is the normally used sampling vector.
x = ((0:M-1)'+cent)/M;
% Use this if window length must be odd or even
Modd = M-mod(M+1,2);
Meven = M-mod(M,2);
xodd = ((0:Modd-1)'+cent)/Modd;
xeven = ((0:Meven-1)'+cent)/Meven;
do_sqrt=0;
switch name
case {'hanning','hann'}
g=(0.5+0.5*cos(2*pi*x));
info.ispu=1;
case {'sine','cosine','sqrthann'}
g=firwin('hanning',M,varargin{:});
info.issqpu=1;
do_sqrt=1;
case {'hamming'}
if cent==0
g=0.54-0.46*cos(2*pi*(xodd-.5));
else
g=0.54-0.46*cos(2*pi*(xeven-.5));
end;
case {'square','rect'}
if cent==0
g=ones(Modd,1);
else
g=ones(Meven,1);
end;
case {'halfsquare','halfrect'}
g=ones(Meven/2,1);
info.ispu=1;
case {'sqrthalfsquare','sqrthalfrect'}
g=ones(Meven/2,1);
info.issqpu=1;
do_sqrt=1;
case {'tria','triangular','bartlett'}
if flags.do_wp
gw=linspace(1,0,Meven/2+1).';
g=[gw;flipud(gw(2:end-1))];
%g=pbspline(M,1,Meven/2,flags.centering);
else
gw=((0:Meven/2-1)/(Meven/2)+0.5).';
g=[gw;flipud(gw)];
end;
info.ispu=1;
case {'sqrttria'}
g=firwin('tria',M,flags.centering);
info.issqpu=1;
do_sqrt=1;
%if flags.do_hp && rem(M,2)==1
% % Remove small error in this case
% g((M+1)/2)=0;
%end;
case {'blackman'}
g=0.42-0.5*cos(2*pi*(x-.5))+0.08*cos(4*pi*(x-.5));
case {'nuttall'}
g = 0.355768 - 0.487396*cos(2*pi*(x-.5)) + 0.144232*cos(4*pi*(x-.5)) -0.012604*cos(6*pi*(x-.5));
case {'itersine','ogg'}
g=sin(pi/2*sin(pi*(x-.5)).^2);
info.issqpu=1;
otherwise
error('Unknown window: %s.',name);
end;
% Add zeros if needed.
if length(g)<M
g=middlepad(g,M,flags.centering);
end;
% Do sqrt if needed. This must be done /after/ middlepad, so do it at
% this point.
if do_sqrt
g=sqrt(g);
end;
if keyvals.taper<1
% Perform the actual tapering.
g=[ones(p1,1);g;ones(p2,1)];
end;
g=normalize(g,flags.norm);