Zero Crossing of Signal - Misunderstanding the attached matlab code.

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Jimmy cho 2020-12-22

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/700637-zero-crossing-of-signal-misunderstanding-the-attached-matlab-code

评论： Star Strider 2021-1-9

Hi guys!

Im trying to understand the zero crossing points that uses interpolation approximation which I found the code here in the threads of matlab.

the code that I found it is this:

x=1:length(y);
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);
% Returns Approximate Zero-Crossing Indices Of Argument Vector
dy = zci(y);
% Indices of Approximate Zero-Crossings
for k1 = 1:size(dy,1)-1
    b = [[1;1] [x(dy(k1)); x(dy(k1)+1)]]\[y(dy(k1)); y(dy(k1)+1)];
    % Linear Fit Near Zero-Crossings
    x0(k1) = -b(1)/b(2);
    % Interpolate ‘Exact’ Zero Crossing
    mb(:,k1) = b;
    % Store Parameter Estimates (Optional)
end

I almost understand the code but I didn't understand the statement of b = [[1;1] [x(dy(k1)); x(dy(k1)+1)]]\[y(dy(k1)); y(dy(k1)+1)]; what does it stand for?

what does this statement mean? I want to understand what this statement does exactly , any help? thanks alot.

does it take a row of matrix and devide it by another row matrix and the result is stored in b? I really just missunderstanding that row among others rows in the code.

all what I need is a detalied explanation what this row b = [[1;1] [x(dy(k1)); x(dy(k1)+1)]]\[y(dy(k1)); is about ? and what it does functionality (takes two rows of matrix and devide between each other?) ?

thanks alot.

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Jimmy cho 2020-12-22

the attached code is taked from this thread:

https://www.mathworks.com/matlabcentral/answers/566015-easy-way-of-finding-zero-crossing-of-a-function

@Star Strider who posted it.

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Answer 1

Star Strider 2020-12-23

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https://ww2.mathworks.cn/matlabcentral/answers/700637-zero-crossing-of-signal-misunderstanding-the-attached-matlab-code#answer_582402

在 MATLAB Online 中打开

Thank you! I recognise my code!

The assignment:

b = [[1;1] [x(dy(k1)); x(dy(k1)+1)]]\[y(dy(k1)); y(dy(k1)+1)];

loops through the zero-crossings returned in ‘dy’ as indexed with ‘k1’ and calculates the linear regression slope and intercept terms for that small segment of the original waveform.

The next line calculates the interpolated value of the exact zero-crossing, and returns it as ‘x0’. The ‘mb’ matrix stores the slope and intercept terms.

For the record, I now use:

zci = @(v) find(diff(sign(v(:))));

since it is a bit more robust and does not have the wrap-around problems my original code for it does.

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Star Strider 2020-12-23

在 MATLAB Online 中打开

Please! I am not online here 24/7 (although it sometimes seems like it). I was sleeping! It is currently 05:35 here (12:35 UCT).

That line derives from calculating linear regressions using the mldivide,\ function (or operator).

This:

b = [[1;1] [x(dy(k1)); x(dy(k1)+1)]]\[y(dy(k1)); y(dy(k1)+1)];

creates the design matrix:

[[1;1] [x(dy(k1)); x(dy(k1)+1)]]

that is equivalent to:

[1  x(dy(k1))
 1  x(dy(k1)+1)]

to create the intercept and slope terms for ‘b’ (in that order, so ‘b(1)’ is the intercept and ‘b(2)’ is the slope) where ‘dy’ are the indices returned by ‘zci’, so it calculates the linear regression between ‘x(dy(k1))’ and the next point in the vector, ‘x(dy(k1))+1)’. It then regresses that against the corresponding points in the dependent variable:

[y(dy(k1)); y(dy(k1)+1)]

Note that it is a column vector.

So, put that together with the information in the documentation link I provided here, and you will understand how that assignment calculation works.

Star Strider 2020-12-23

在 MATLAB Online 中打开

‘Another question, I still confused why I need this row code:’

dy = zci(y);

My ‘zci’ function find the ap[proximate indices of the zero-crossings. I wrote it as a function to make it easier to use. Any vector will work for ‘v’, and here I used ‘y’, since only the dependent variable should have a significant number of zero-crossings.

‘Another question, does the size of

b = [[1;1] [x(dy(k1)); x(dy(k1)+1)]]\[y(dy(k1)); y(dy(k1)+1)];

is constant and isn't related to the size of the given input? I mean always the size of [[1;1] [x(dy(k1)); x(dy(k1)+1)]] is 2x2 and the size of [y(dy(k1)); y(dy(k1)+1)] 1x2 ?’

Yes. It only calculates the intercept and slope for the two adjacent points, then calculates a much more precise estimate for the actual zero-crossings from them, assuming that ‘y’ in that region is acceptably linear. (I could have used other functions, such as polyfit for the slope and intercept, or interp1 aloone to find the zero crossings, however the approach using the linear regression using mldivide is faster and more efficient.)