BOSC.tf

function [B,T,P]=BOSC_tf(eegsignal,F,Fsample,wavenumber)
% [B,T,P]=BOSC_tf(eegsignal,F,Fsample,wavenumber);
%
% This function computes a continuous wavelet (Morlet) transform on
% a segment of EEG signal; this can be used to estimate the
% background spectrum (BOSC_bgfit) or to apply the BOSC method to
% detect oscillatory episodes in signal of interest (BOSC_detect).
%
% parameters:
% eegsignal - a row vector containing a segment of EEG signal to be
%             transformed
% F - a set of frequencies to sample (Hz)
% Fsample - sampling rate of the time-domain signal (Hz)
% wavenumber is the size of the wavelet (typically, width=6)
%	
% returns:
% B - time-frequency spectrogram: power as a function of frequency
%     (rows) and time (columns)
% T - vector of time values (based on sampling rate, Fsample)
% P - estimated phase for each point in time and for each frequency - KEM 2014

st=1./(2*pi*(F/wavenumber));
A=1./sqrt(st*sqrt(pi));
B = zeros(length(F),length(eegsignal)); % initialize the time-frequency matrix
P = B;
for f=1:length(F) % loop through sampled frequencies
  t=-3.6*st(f):(1/Fsample):3.6*st(f);
  m=A(f)*exp(-t.^2/(2*st(f)^2)).*exp(1i*2*pi*F(f).*t); % Morlet wavelet
  
  y=conv(eegsignal,m,'same'); 
  P(f,:) = angle(y); 
  B(f,:) = abs(y).^2;
end
T=(1:size(eegsignal,2))/Fsample;


%    This file is part of the Better OSCillation detection (BOSC) library.
%
%    The BOSC library 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.
%
%    The BOSC library 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 Foobar.  If not, see <http://www.gnu.org/licenses/>.
%
%    Copyright 2010 Jeremy B. Caplan, Adam M. Hughes, Tara A. Whitten
%    and Clayton T. Dickson.