Zero-crossing calculation

Hi all, I need a script which can calculate zero crossing of the signal. I have the value of x and y. The script should be able to calculate the exact position of zero crossing points. Help!

Answer 1

[Star Strider]

This is reasonably robust:

function ZC = ZeroX(x,y)
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
zxidx = zci(y);
for k1 = 1:numel(zxidx)
    idxrng = max([1 zxidx(k1)-1]):min([zxidx(k1)+1 numel(y)]);
    xrng = x(idxrng);
    yrng = y(idxrng);
    ZC(k1) = interp1( yrng(:), xrng(:), 0, 'linear', 'extrap' );
end
end

x = linspace(0, 11*pi, 42);                                             % Create Data
y = sin(x);                                                             % Create Data

ZC = ZeroX(x,y);

figure(1)
plot(x, y, '-r')
hold on
plot(ZC, zeros(size(ZC)), 'pg')
hold off
grid

[Jayanta Deb]

thanks Star... brilliant... cheers, Jayanta

[Star Strider]

As always, my pleasure!

Thank you!

[hanadi abbas]

thank you

[Ike Brown]

Thanks for posting this Star Strider! I found this very helpful. Here is a slight modification in order to avoid the following error "grid vectors not strictly monotonic increasing". This modification is based off of a forum answer by Jos (10584)

% ZeroX has been modified so as to avoid the following error "Error using griddedInterpolant
% The grid vectors are not strictly monotonic increasing."
%
% The following modifications are based off of this MatLab forum answer:
% https://www.mathworks.com/matlabcentral/answers/283718-grid-vectors-not-strictly-monotonic-increasing

function ZC = ZeroX(x,y)
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0); % Returns Approximate Zero-Crossing Indices Of Argument Vector
zxidx = zci(y);
for k1 = 1:numel(zxidx)
    idxrng = max([1 zxidx(k1)-1]):min([zxidx(k1)+1 numel(y)]);
    xrng = x(idxrng);
    yrng = y(idxrng);
    
    % Beginning of ZeroX2 modifications. The naming conventions follow
    % those in the referenced MatLab forum, except that "X" is "yrng" and
    % "Y" is "xrng".
    [yrng2, ~, jyrng] = unique(yrng); %yrng is a new array containing the unique values of yrng. jyrng contains the indices in yrng that correspond to the original vector. yrng = yrng2(jyrng)
    xrng2 = accumarray(jyrng, xrng, [], @mean); %This function creates a new array "xrng2" by applying the function "@mean" to all elements in "xrng" that have identical indices in "jyrng". Any elements with identical X values will have identical indices in jyrng. Thus, this function creates a new array by averaging values with identical X values in the original array.
        
    ZC(k1) = interp1( yrng2(:), xrng2(:), 0, 'linear', 'extrap' );
    
end
end

[GIULIA CISOTTO]

Dear Ike Brown,

thank you for sharing your code. However, I would like to let you know that it seems to incorrectly detect ZC points.

I wrote an alternative Matlab script (myZC.m) to find the ZC. Here, you can find it.

To test the difference between ZeroX and myZC, you can run a modified version of your toy example as follows:

rng(shuffle)

x = linspace(0, 11*pi, 42);     % Create Data
y = sin(x);                     % Create Data

n = 1 + 2.*randn(1,length(y));  % add Gaussian noise
y = y+n;


% myZC
[myZC, myZCx, myZCy, ys] = myZC(x,y);


% Comparison with ZeroX
ZC = ZeroX(x,y);



% Print ZC values
[length(myZC), length(ZC)]



% Plot figure
figure, hold all
plot(x,y,'k'), xlabel('No. samples'), ylabel('Amplitude [A.U.]')
plot(x,ys,'b:') 
plot(x(myZC), zeros(size(myZC)), 'bs', 'markerface', 'b')
plot(myZCx, myZCy, 'cd', 'markerface', 'c')
plot(ZC, zeros(size(ZC)), 'pr'), grigrid on, legend('y', 'ys', 'myZC', 'myZC-refined', 'ZC')

In attach, you can also find a representative plot: you can notice that ZeroX can mostly correctly detect the zero-crossigs, but sometimes it misses one (between sample no.17 and sample no.18) or it detects a false one (at sample 27).

ZeroX returns a correct number of zero-crossings, but when plotted, they are mismatched to the raw signal, while myZC can correctly compute the number of zero-crossing and precisely get their locations.

Answer 2

[MSP]

zeroindex=find(y==0)
x(zeroindex)

[Jayanta Deb]

Thanks MSP

cheers, Jayanta

[Shubhashree Bal]

It is not necessary that there is sample at amplitude equal to 0.

Example:

x = [ 1 2 3 4 5];

y = [1 -1 -2 -3 -4];

k= find (y==0);

Conclusion: Instead of having zero crossing it will not return any index. Thus, we can check sign change for finding zero crossing accurately.

Thanks!

[GIULIA CISOTTO]

Dear Shubhashree, this is not actually true: zero-crossing is defined as the number of times a signal changes its sign. If you apply your computation, then you might have an incorrect number of ZC. Let's consider a signal with a number of consecutive samples set to zero: then, you will add all of them to the ZC counter. However, you would be wrong in that. Please, check my answer above for the correct computation of ZC.