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function [st,t,f] = st(timeseries,factor,minfreq,maxfreq,samplingrate,freqsamplingrate) % Returns the Stockwell Transform of the timeseries. % Code by Robert Glenn Stockwell. % DO NOT DISTRIBUTE % BETA TEST ONLY % Reference is "Localization of the Complex Spectrum: The S Transform" % from IEEE Transactions on Signal Processing, vol. 44., number 4, April 1996, pages 998-1001. % %-------Inputs Needed------------------------------------------------ % % *****All frequencies in (cycles/(time unit))!****** % "timeseries" - vector of data to be transformed %-------Optional Inputs ------------------------------------------------ % %"minfreq" is the minimum frequency in the ST result(Default=0) %"maxfreq" is the maximum frequency in the ST result (Default=Nyquist) %"samplingrate" is the time interval between samples (Default=1) %"freqsamplingrate" is the frequency-sampling interval you desire in the ST result (Default=1) %Passing a negative number will give the default ex. [s,t,f] = st(data,-1,-1,2,2) %-------Outputs Returned------------------------------------------------ % % st -a complex matrix containing the Stockwell transform. % The rows of STOutput are the frequencies and the % columns are the time values ie each column is % the "local spectrum" for that point in time % t - a vector containing the sampled times % f - a vector containing the sampled frequencies %--------Additional details----------------------- % % There are several parameters immediately below that % the user may change. They are: %[verbose] if true prints out informational messages throughout the function. %[removeedge] if true, removes a least squares fit parabola % and puts a 5% hanning taper on the edges of the time series. % This is usually a good idea. %[analytic_signal] if the timeseries is real-valued % this takes the analytic signal and STs it. % This is almost always a good idea. %[factor] the width factor of the localizing gaussian % ie, a sinusoid of period 10 seconds has a % gaussian window of width factor*10 seconds. % I usually use factor=1, but sometimes factor = 3 % to get better frequency resolution. % Copyright (c) by Bob Stockwell % $Revision: 1.2 $ $Date: 1997/07/08 $ % This is the S transform wrapper that holds default values for the function. TRUE = 1; FALSE = 0; %%% DEFAULT PARAMETERS [change these for your particular application] verbose = TRUE; removeedge= FALSE; analytic_signal = FALSE; factor = factor;%default - 1 %%% END of DEFAULT PARAMETERS %%%START OF INPUT VARIABLE CHECK % First: make sure it is a valid time_series % If not, return the help message if verbose disp(' '),end % i like a line left blank if nargin == 0 if verbose disp('No parameters inputted.'),end st_help t=0;,st=-1;,f=0; return end % Change to column vector if size(timeseries,2) > size(timeseries,1) timeseries=timeseries'; end % Make sure it is a 1-dimensional array if size(timeseries,2) > 1 error('Please enter a *vector* of data, not matrix') return elseif (size(timeseries)==[1 1]) == 1 error('Please enter a *vector* of data, not a scalar') return end % use defaults for input variables if nargin == 1 minfreq = 0; maxfreq = fix(length(timeseries)/2); samplingrate=1; freqsamplingrate=1; elseif nargin==3 maxfreq = fix(length(timeseries)/2); samplingrate=1; freqsamplingrate=1; [ minfreq,maxfreq,samplingrate,freqsamplingrate] = check_input(minfreq,maxfreq,samplingrate,freqsamplingrate,verbose,timeseries); elseif nargin==4 samplingrate=1; freqsamplingrate=1; [ minfreq,maxfreq,samplingrate,freqsamplingrate] = check_input(minfreq,maxfreq,samplingrate,freqsamplingrate,verbose,timeseries); elseif nargin==5 freqsamplingrate=1; [ minfreq,maxfreq,samplingrate,freqsamplingrate] = check_input(minfreq,maxfreq,samplingrate,freqsamplingrate,verbose,timeseries); elseif nargin == 6 [ minfreq,maxfreq,samplingrate,freqsamplingrate] = check_input(minfreq,maxfreq,samplingrate,freqsamplingrate,verbose,timeseries); else if verbose disp('Error in input arguments: using defaults'),end minfreq = 0; maxfreq = fix(length(timeseries)/2); samplingrate=1; freqsamplingrate=1; end if verbose disp(sprintf('Minfreq = %d',minfreq)) disp(sprintf('Maxfreq = %d',maxfreq)) disp(sprintf('Sampling Rate (time domain) = %d',samplingrate)) disp(sprintf('Sampling Rate (freq. domain) = %d',freqsamplingrate)) disp(sprintf('The length of the timeseries is %d points',length(timeseries))) disp(' ') end %END OF INPUT VARIABLE CHECK % If you want to "hardwire" minfreq & maxfreq & samplingrate & freqsamplingrate do it here % calculate the sampled time and frequency values from the two sampling rates t = (0:length(timeseries)-1)*samplingrate; spe_nelements =ceil((maxfreq - minfreq+1)/freqsamplingrate) ; f = (minfreq + [0:spe_nelements-1]*freqsamplingrate)/(samplingrate*length(timeseries)); if verbose disp(sprintf('The number of frequency voices is %d',spe_nelements)),end % The actual S Transform function is here: st = strans(timeseries,minfreq,maxfreq,samplingrate,freqsamplingrate,verbose,removeedge,analytic_signal,factor); % this function is below, thus nicely encapsulated %WRITE switch statement on nargout % if 0 then plot amplitude spectrum if nargout==0 if verbose disp('Plotting pseudocolor image'),end pcolor(t,f,abs(st)) end return %^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ %^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ %^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ %^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ %^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ function st = strans(timeseries,minfreq,maxfreq,samplingrate,freqsamplingrate,verbose,removeedge,analytic_signal,factor); % Returns the Stockwell Transform, STOutput, of the time-series % Code by R.G. Stockwell. % Reference is "Localization of the Complex Spectrum: The S Transform" % from IEEE Transactions on Signal Processing, vol. 44., number 4, % April 1996, pages 998-1001. % %-------Inputs Returned------------------------------------------------ % - are all taken care of in the wrapper function above % %-------Outputs Returned------------------------------------------------ % % ST -a complex matrix containing the Stockwell transform. % The rows of STOutput are the frequencies and the % columns are the time values % % %----------------------------------------------------------------------- % Compute the length of the data. n=length(timeseries); original = timeseries; if removeedge if verbose disp('Removing trend with polynomial fit'),end ind = [0:n-1]'; r = polyfit(ind,timeseries,2); fit = polyval(r,ind) ; timeseries = timeseries - fit; if verbose disp('Removing edges with 5% hanning taper'),end sh_len = floor(length(timeseries)/100);%default timeseries/10 wn = hanning(sh_len); if(sh_len==0) sh_len=length(timeseries); wn = 1&[1:sh_len]; end % make sure wn is a column vector, because timeseries is if size(wn,2) > size(wn,1) wn=wn'; end timeseries(1:floor(sh_len/2),1) = timeseries(1:floor(sh_len/2),1).*wn(1:floor(sh_len/2),1); timeseries(length(timeseries)-floor(sh_len/2):n,1) = timeseries(length(timeseries)-floor(sh_len/2):n,1).*wn(sh_len-floor(sh_len/2):sh_len,1); end % If vector is real, do the analytic signal if analy