Is it possible to determine the angle of rotation for this graph?

I have a graph with two curves which depicts the rotated version of the each other. How can I determine the curve is shifted from one another? Atleast is there a technique to find by how much bins its the curves are rotated?

[Walter Roberson]

If they differ only in one having a phase shift, then their fft() should be the same except with different imaginary coefficients (phase is encoded in imaginary coefficients)

[Image Analyst]

They are not rotated. It looks like there is a shift of the plot along the x direction. Perhaps you could use xcorr() but I think the lag might be too much and there is not enough signal that is the same between the two. Are they exact copies, just shifted, or just roughly the same shape?

[NAVYA MOHAN]

They are not having phase shift .. i tried using fft and xcorr yielding zero phase shift.

They are exact copies but rotated by some angle.. ie values are rotated randomly starting at any position but they maintain the order (like this shown)

x= [1 2 3 4 5 6 7 8 9 10]

y = [5 6 7 8 9 10 1 2 3 4]

I would like to know how much it is rotated? is there any technique with which can find the rotation with respect to a ref point?

[Walter Roberson]

The plots you show are not just a circular shift of each other. The magnitudes are clearly quite different.

Answer 1

[Bjorn Gustavsson]

If you have your signals in y1 and y2 you can try to use circshift with an incremental shift until you see a reasonable fit. You can just do it in a simlpe loop:

for i1 = 1:numel(y1)
    plot([y1;circshift(y2,i1-1)])
    title(i1)
    disp('push any key to continue')
    pause
end

HTH

Answer 2

[Walter Roberson]

If one really was a circshift of the other, then by taking one and repeating it once, you can be sure that it would have a substring that was exactly the other one, and the offset to that substring would be the shift value. You would be able to use strfind() to locate the copy.

But there is no way that the example plots are simple circular shifts of each other.

[Bjorn Gustavsson]

I beg to disagree, shift the redish curve ~250 steps forward and I think you'll get a reasonable fit.

[Walter Roberson]

Ah, I missed that part of the graph.

[NAVYA MOHAN]

Its actually circular shift .. i checked the values.. and used the function circshift..

Thank You!