Pattern extraction from a signal

I am trying to get all the patterns that could be extracted from my signal. I could extract patterns by defining a threshold and only taking part of signal that crosses the threshold. But to use this approach, I need to define the sample/time difference between each pattern beforehand. Furhtermore I have lot of zero-crossing in the signal and there is no trend in the amplitude either. Is there any approcah where I can just extract all the patterns straightforwardly without using thershold or time difference. I have also attached my signal and patterns that I got using the threshold approach.

Thanks.

[Image Analyst]

Maybe envelope() or boundary()?

[rizal_m]

Thanks for the input. I have tried envelope() before but patterns depends on size of sliding window or sample size and as each pattern has a numbers of zero-crossing I am not getting the expected results. I haven't tried the boundary function yet. I will give it a try and see.

Thanks.

[Walter Roberson]

When you do not have hard rules about the boundaries, then the number of patterns is related to Partition Theory https://en.wikipedia.org/wiki/Partition_function_(number_theory) and becomes huge as the signal grows modestly in length.

[Mathieu NOE]

hi

can you make a decision based on spectral content ? if you were to do a spectrogram , can you select the patterns because a certain rule based on amplitude / frequency can be used ?

otherwise , I would too have used a kind of envelope and zero crossing detection

Answer 1

[Mathieu NOE]

hello

maybe this ? (already discussed above)

clc
clearvars

% dummy signal
n=1000;
x=linspace(0,2*pi*3,n);
y = 0.25*randn(size(x));
y(100:199) = randn(1,100);
y(400:499) = randn(1,100);
y(600:699) = randn(1,100);

% home made envelope
env = smoothdata(abs(y),'gaussian',100);

threshold = 0.25*max(env)+0.75*min(env); % your value here

[t0_pos,s0_pos,t0_neg,s0_neg]= crossing_V7(env,x,threshold,'linear'); % positive (pos) and negative (neg) slope crossing points 
% ind => time index (samples)
% t0 => corresponding time (x) values 
% s0 => corresponding function (y) values , obviously they must be equal to "threshold"

figure(1)
plot(x,y,x,env,x,threshold*ones(size(x)),'k--',t0_pos,s0_pos,'dr',t0_neg,s0_neg,'dg','linewidth',2,'markersize',12);grid on
legend('signal',' my envelope','threshold','positive slope crossing points','negative slope crossing points');

period = diff(t0_pos)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [t0_pos,s0_pos,t0_neg,s0_neg] = crossing_V7(S,t,level,imeth)

% [ind,t0,s0,t0close,s0close] = crossing_V6(S,t,level,imeth,slope_sign) % older format

% CROSSING find the crossings of a given level of a signal
%   ind = CROSSING(S) returns an index vector ind, the signal
%   S crosses zero at ind or at between ind and ind+1
%   [ind,t0] = CROSSING(S,t) additionally returns a time
%   vector t0 of the zero crossings of the signal S. The crossing
%   times are linearly interpolated between the given times t
%   [ind,t0] = CROSSING(S,t,level) returns the crossings of the
%   given level instead of the zero crossings
%   ind = CROSSING(S,[],level) as above but without time interpolation
%   [ind,t0] = CROSSING(S,t,level,par) allows additional parameters
%   par = {'none'|'linear'}.
%	With interpolation turned off (par = 'none') this function always
%	returns the value left of the zero (the data point thats nearest
%   to the zero AND smaller than the zero crossing).
%


% check the number of input arguments
error(nargchk(1,4,nargin));

% check the time vector input for consistency
if nargin < 2 | isempty(t)
	% if no time vector is given, use the index vector as time
    t = 1:length(S);
elseif length(t) ~= length(S)
	% if S and t are not of the same length, throw an error
    error('t and S must be of identical length!');    
end

% check the level input
if nargin < 3
	% set standard value 0, if level is not given
    level = 0;
end

% check interpolation method input
if nargin < 4
    imeth = 'linear';
end


% make row vectors
t = t(:)';
S = S(:)';

% always search for zeros. So if we want the crossing of 
% any other threshold value "level", we subtract it from
% the values and search for zeros.
S   = S - level;

% first look for exact zeros
ind0 = find( S == 0 ); 

% then look for zero crossings between data points
S1 = S(1:end-1) .* S(2:end);
ind1 = find( S1 < 0 );

% bring exact zeros and "in-between" zeros together 
ind = sort([ind0 ind1]);

% and pick the associated time values
t0 = t(ind); 
s0 = S(ind);

if ~isempty(ind)

    if strcmp(imeth,'linear')
        % linear interpolation of crossing
        for ii=1:length(t0)
            %if abs(S(ind(ii))) >= eps(S(ind(ii)))    % MATLAB V7 et +
            if abs(S(ind(ii))) >= eps*abs(S(ind(ii)))    % MATLAB V6 et -    EPS * ABS(X)

                % interpolate only when data point is not already zero
                NUM = (t(ind(ii)+1) - t(ind(ii)));
                DEN = (S(ind(ii)+1) - S(ind(ii)));
                slope =  NUM / DEN;
                slope_sign(ii) = sign(slope);
                t0(ii) = t0(ii) - S(ind(ii)) * slope;
                s0(ii) = level;
            end
        end
    end

    % extract the positive slope crossing points 
    ind_pos = find(sign(slope_sign)>0);
    t0_pos = t0(ind_pos);
    s0_pos = s0(ind_pos);

    % extract the negative slope crossing points 
    ind_neg = find(sign(slope_sign)<0);
    t0_neg = t0(ind_neg);
    s0_neg = s0(ind_neg);

else

    % empty output
    ind_pos = [];
    t0_pos = [];
    s0_pos = [];

    % extract the negative slope crossing points 
    ind_neg = [];
    t0_neg = [];
    s0_neg = [];
    
end

end