% DFTFILT3 - discrete complex wavelet filters
%
% Usage:
% >> [wavelet,cycles,freqresol,timeresol] = dftfilt3( freqs, cycles, srate, varargin)
%
% Inputs:
% freqs - vector of frequencies of interest.
% cycles - cycles array. If cycles=0, then the Hanning tapered Short-term FFT is used.
% If one value is given and cycles>0, all wavelets have
% the same number of cycles. If two values are given, the
% two values are used for the number of cycles at the lowest
% frequency and at the highest frequency, with linear or
% log-linear interpolation between these values for intermediate
% frequencies
% srate - sampling rate (in Hz)
%
% Optional Inputs: Input these as 'key/value pairs.
% 'cycleinc' - ['linear'|'log'] increase mode if [min max] cycles is
% provided in 'cycle' parameter. {default: 'linear'}
% 'winsize' Use this option for Hanning tapered FFT or if you prefer to set the length of the
% wavelets to be equal for all of them (e.g., to set the
% length to 256 samples input: 'winsize',256). {default: [])
% Note: the output 'wavelet' will be a matrix and it may be
% incompatible with current versions of timefreq and newtimef.
% 'timesupport' The number of temporal standard deviation used for wavelet lengths {default: 7)
%
% Output:
% wavelet - cell array or matrix of wavelet filters
% timeresol - temporal resolution of Morlet wavelets.
% freqresol - frequency resolution of Morlet wavelets.
%
% Note: The length of the window is always made odd.
%
% Authors: Arnaud Delorme, SCCN/INC/UCSD, La Jolla, 3/28/2003
% Rey Ramirez, SCCN/INC/UCSD, La Jolla, 9/26/2006
% Copyright (C) 3/28/2003 Arnaud Delorme 8, SCCN/INC/UCSD, arno@salk.edu
%
% This file is part of EEGLAB, see http://www.eeglab.org
% for the documentation and details.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
%
% 1. Redistributions of source code must retain the above copyright notice,
% this list of conditions and the following disclaimer.
%
% 2. Redistributions in binary form must reproduce the above copyright notice,
% this list of conditions and the following disclaimer in the documentation
% and/or other materials provided with the distribution.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
% THE POSSIBILITY OF SUCH DAMAGE.
%
% Revision 1.12 2006/09/25 rey r
% Almost complete rewriting of dftfilt2.m, changing both Morlet and Hanning
% DFT to be more in line with conventional implementations.
%
% Revision 1.11 2006/09/07 19:05:34 scott
% further clarified the Morlet/Hanning distinction -sm
%
% Revision 1.10 2006/09/07 18:55:15 scott
% clarified window types in help msg -sm
%
% Revision 1.9 2006/05/05 16:17:36 arno
% implementing cycle array
%
% Revision 1.8 2004/03/04 19:31:03 arno
% email
%
% Revision 1.7 2004/02/25 01:45:55 arno
% sinus test
%
% Revision 1.6 2004/02/15 22:23:08 arno
% implementing morlet wavelet
%
% Revision 1.5 2003/05/09 20:55:10 arno
% adding hanning function
%
% Revision 1.4 2003/04/29 16:02:54 arno
% header typos
%
% Revision 1.3 2003/04/29 01:09:16 arno
% debug imaginary part
%
% Revision 1.2 2003/04/28 23:01:13 arno
% *** empty log message ***
%
% Revision 1.1 2003/04/28 22:46:49 arno
% Initial revision
%
function [wavelet,cycles,freqresol,timeresol] = dftfilt3( freqs, cycles, srate, varargin);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Rey fixed all input parameter sorting.
if nargin < 3
error(' A minimum of 3 arguments is required');
end
numargin=length(varargin);
if rem(numargin,2)
error('There is an uneven number key/value inputs. You are probably missing a keyword or its value.')
end
varargin(1:2:end)=lower(varargin(1:2:end));
% Setting default parameter values.
cycleinc='linear';
winsize=[];
timesupport=7; % Setting default of 7 temporal standard deviations for wavelet's length.
for n=1:2:numargin
keyword=varargin{n};
if strcmpi('cycleinc',keyword)
cycleinc=varargin{n+1};
elseif strcmpi('winsize',keyword)
winsize=varargin{n+1};
if ~mod(winsize,2)
winsize=winsize+1; % Always set to odd length wavelets and hanning windows;
end
elseif strcmpi('timesupport',keyword)
timesupport=varargin{n+1};
else
error(['What is ' keyword '? The only legal keywords are: type, cycleinc, winsize, or timesupport.'])
end
end
if isempty(winsize) && cycles(1)==0
error('If you are using a Hanning tapered FFT, please supply the winsize input-pair.')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% compute number of cycles at each frequency
% ------------------------------------------
type='morlet';
if length(cycles) == 1 && cycles(1)~=0
cycles = cycles*ones(size(freqs));
elseif length(cycles) == 2
if strcmpi(cycleinc, 'log') % cycleinc
cycles = linspace(log(cycles(1)), log(cycles(2)), length(freqs));
cycles = exp(cycles);
%cycles=logspace(log10(cycles(1)),log10(cycles(2)),length(freqs)); %rey
else
cycles = linspace(cycles(1), cycles(2), length(freqs));
end
end
if cycles==0
type='sinus';
end
sp=1/srate; % Rey added this line (i.e., sampling period).
% compute wavelet
for index = 1:length(freqs)
fk=freqs(index);
if strcmpi(type, 'morlet') % Morlet.
fk=fk/srate; % Normalize frequency for textbook equations as in TB97
sigf=fk/cycles(index); % Computing time and frequency standard deviations, resolutions, and normalization constant.
sigt=1./(2*pi*sigf);
A=1./sqrt(sigt*sqrt(pi));
timeresol(index)=2*sigt/srate; % sec
freqresol(index)=2*sigf*srate; % Hz
if isempty(winsize) % bases will be a cell array.
% tneg=[-sp:-sp:-sigt*timesupport/2];
% tpos=[0:sp:sigt*timesupport/2];
% t=[fliplr(tneg) tpos];
t = (0:floor(sigt*timesupport/2)*2)-floor(sigt*timesupport/2); % Always odd; backward compatible
psi=A.*(exp(-(t.^2)./(2*(sigt^2))).*exp(2*i*pi*fk*t));
wavelet{index}=psi; % These are the wavelets with variable number of samples based on temporal standard deviations (sigt).
else % bases will be a matrix.
% tneg=[-sp:-sp:-sp*winsize/2];
% tpos=[0:sp:sp*winsize/2];
% t=[fliplr(tneg) tpos];
t = (0:floor(winsize/2)*2)-floor(winsize/2); % Always odd; backward compatible
psi=A.*(exp(-(t.^2)./(2*(sigt^2))).*exp(2*i*pi*fk*t));
wavelet(index,:)=psi; % These are the wavelets with the same length.
% This is useful for doing time-frequency analysis as a matrix vector or matrix matrix multiplication.
end
elseif strcmpi(type, 'sinus') % Hanning
tneg=[-sp:-sp:-sp*winsize/2];
tpos=[0:sp:sp*winsize/2];
t=[fliplr(tneg) tpos];
win = exp(2*i*pi*fk*t);
wavelet(index,:) = win .* hanning(winsize)';
%wavelet{index} = win .* hanning(winsize)';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
end
% symmetric hanning function
function w = hanning(n)
if ~rem(n,2)
w = .5*(1 - cos(2*pi*(1:n/2)'/(n+1)));
w = [w; w(end:-1:1)];
else
w = .5*(1 - cos(2*pi*(1:(n+1)/2)'/(n+1)));
w = [w; w(end-1:-1:1)];
end
Datasets
Models
