Identify Zerocrossing Indices near to the peak of the other signal matlab

Hi all, I have two signals (data attached) , for first signal I plot the peaks of the signal and for the second one I find zero crossings of the signal. My aim is to find the zero crossing indices (start and stop) closer to the peak of the first signal. In this example (please refer to the figure), peak for the first signal is around 4.567 and the zerocrossings (closest ones) are closer to 4.564 and 4.571 respectively. I would like to get these indices (start and stop) for the signal with all the peak points. For your reference, I have added data, code for peak and zerocrossing and also figure.

https://www.dropbox.com/s/i8s52no5ivdo6gm/data.mat?dl=0

Any help in this regard is highly appreciated.

load Data.mat;
t=1:length(Data(:,1));
[pk,lk] = findpeaks(Data(:,1),t,'MinPeakProminence',200);
ax1=subplot(211); 
plot(t,Data(:,1),lk,pk,'o')
                                                   
y = Data(:,2);                                                        
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    
zx = zci(y);  % Approximate Zero-Crossing Indices
figure(1); 
ax2=subplot(212)
plot(t, y, '-r')
hold on
plot(t(zx), y(zx), 'bp'); hold on;
% plot(t,Pepi);
hold off
grid
legend('Signal', 'Approximate Zero-Crossings')
linkaxes([ax1 ax2],'x')

Answer 1

[Star Strider]

The file is too large to download here, and the online Run feature still has problems with .mat files.

That aside, finding the zero-crossings (using simulated data) is straightforward

t = linspace(0, 10, 500);
s = sum((1:10)'.*(sin((1:10)'*pi*t)));

zxi = find(diff(sign(s)));                                                  % Approximate Zero-Crossing Indices

for k = 1:numel(zxi)
    idxrng = max(1,zxi(k)-2) : min(numel(s),zxi(k)+2);
    t_exact(k) = interp1(s(idxrng), t(idxrng), 0);
end

t_exact

t_exact = 1×100

0 0.1367 0.2346 0.3311 0.4270 0.5226 0.6180 0.7136 0.8092 0.9047 0.9999 1.0953 1.1909 1.2865 1.3819 1.4773 1.5730 1.6691 1.7656 1.8637 1.9999 2.1370 2.2348 2.3312 2.4269 2.5224 2.6181 2.7137 2.8092 2.9045

figure
plot(t, s)
hold on
plot(t(zxi), s(zxi), 'xg')
plot(t_exact, zeros(size(t_exact)), '+r')
hold off
grid
legend('Signal','Approximate Zero-Crossing Indices','Interpolated Exact Zero-Crossings', 'Location','best')

figure
plot(t, s)
hold on
plot(t(zxi), s(zxi), 'sg', 'MarkerSize',10)
plot(t_exact, zeros(size(t_exact)), 'xr', 'MarkerSize',10)
hold off
grid
legend('Signal','Approximate Zero-Crossing Indices','Interpolated Exact Zero-Crossings', 'Location','best')
xlim([3  5])

I changed the zero-crossing index code from my previous posts. The one I use here is more robust and does not encounter the ‘wrap-around’ problems of my original version.

.

[Ganesh Naik]

Hi Star Strider, thanks for your answer. To make it clear, I have two different signals: a) Using signal one I obtain peaks, b) Signal 2 is bit noisy data where there are several zero crossing points. My aim is to pick two zero crossing points (start and end) from signal 2 for each peak of signal 1. I have now stored original data in .CSV format (which also contain less data as compared to the original data).

https://www.dropbox.com/s/r54hvh3fvbbrcs1/Data.csv?dl=0

Any suggestion/help is highly appreciated.

[Star Strider]

My pleasure!

The term ‘peaks’ is a bit ambiguous her, since there are several. For the time being, I assume you are referring to the two largest peaks, so I will proceed from there.

The first step with a noisy signal is to filter it, and the easiest way to do that (considering that this appears to be broadband noise) is to use the sgolayfilt function.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1012870/Data.csv', 'VariableNamingRule','preserve');
T1.Properties.VariableNames = {'S1','S2'}

T1 = 99999×2 table
      S1         S2   
    _______    _______

     -1.644     0.2883
    -1.6658    0.32344
    -1.7094    0.32932
    -1.6876    0.31491
    -1.6222    0.27829
    -1.6004    0.27442
    -1.6004    0.28124
    -1.5132     0.2926
    -1.5786    0.30107
    -1.5786    0.30266
    -1.6004    0.29773
    -1.6222    0.29006
    -1.5568    0.28383
    -1.5786    0.28203
    -1.4696     0.2846
    -1.6004    0.28918

t = linspace(0, size(T1,1)-1, size(T1,1));
S1S2F = sgolayfilt(T1{:,[1 2]}, 3, 501);
S1F = S1S2F(:,1);
S2F = S1S2F(:,2);

figure
plot(t, T1{:,[1 2]})
grid
legend('S1','S2', 'Location','best')

figure
plot(t, S1S2F)
grid
legend('S1F','S2F', 'Location','best')

s = S2F;
zxi = find(diff(sign(s)));                                                  % Approximate Zero-Crossing Indices

for k = 1:numel(zxi)
    idxrng = max(1,zxi(k)-2) : min(numel(s),zxi(k)+2);
    t_exact(k) = interp1(s(idxrng), t(idxrng), 0);
end

% t_exact

[pks,locs] = findpeaks(S1F, 'MinPeakProminence',50);

for k = 1:numel(locs)
    te(k,1) = find(t_exact>t(locs(k)),1,'first');
    te(k,2) = find(t_exact<t(locs(k)),1,'last');
end


figure
plot(t, s)
hold on
plot(t(zxi), s(zxi), 'xg')
plot(t_exact, zeros(size(t_exact)), '+r')
hold off
grid
legend('Signal','Approximate Zero-Crossing Indices','Interpolated Exact Zero-Crossings', 'Location','best')

figure
for k = 1:numel(locs)
    win = 1000;
    idxrng = max(1,locs(k)- win) : min(numel(t),locs(k)+win);
    subplot(2,1,k)
    yyaxis left
    plot(t(idxrng), S1F(idxrng))
    yyaxis right
    hold on
    plot(t(idxrng), S2F(idxrng))
    plot(t_exact(te(k,:)), zeros(size(te(k,:))), 'sg', 'MArkerSize',10)
    yline(0, '--r')
    hold off
    grid
    text(t_exact(te(k,:)), zeros(size(te(k,:))), compose('t = %10.2f \\rightarrow', t_exact(te(k,:))), 'Horiz','right', 'Vert','middle', 'Rotation',90, 'FontSize',9)
end

.

[Ganesh Naik]

Dear Star Strider you are the legend. Now I have managed to get the start and stop of corresponding second signal for every peak location of the first signal. I have tested this for a large data with 12 peak locations. Now i will work on it to shade/patch start stop locations.

Index = fliplr(te) % Get the start stop indexes 
Start_Stop = t_exact(Index)

Thanks again for your help, much appreciated.

[Star Strider]

As always, my pleasure!

Answer 2

[KSSV]

Multiple options:

1. Use knnsearch
2. Use interp1
3. Use InterX: https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections

I would suggest to use third option.

[Ganesh Naik]

Hi KSSV thanks for your answer. I have two separate signals. Signal 1 generates peak points and signal 2 is a noisy signal and from it I get several zero crossing points. My aim is to pick up two closest zero crossing points from signal 2 for every peak of signal 1. Unfortunately signal 1 and signal 2 dont intersects and hence I cant use the third option that you suggested.