Thread: Fitting a sine wave between two lines

I have a data set that appears to be made up of two linear regions, separated by what best looks like a sine wave.



I know the x and y co-ordinates of the two points at the end of each line segment, x1, x2, y1, y2, and the respective gradient of the lines, m1 and m2.

I believe I can parameterise a sine wave of the form "y = Asin(Bx+C)+D" so that it passes through the given points, with the same gradient, but can't work out how to solve for the parameters.

Does anybody have any ideas?
Thanks!

Hi !
The shape of the curve looks like an hyperbola (non orthogonal).
I suggest to fit the curve (least squares fitting method, involving 5 parameters) to the general quadratic equation and then, compute the characteristic parameters of the hyperbola.
It might be much simpler if you already know the gradient of the asymtotes m1 and m2 . In this case, the equation of the hyperbola is :
(y-m1*x+C1)*(y-m2*x+C2)+C3=0
C1, C2 and C3 can be computed thanks to a linear regression involving 3 parameters (to be defined in relation with C1, C2, C3).

Hi,

This works, thanks for the reply!

If anyone has any ideas, I'd still be interested to know whether it's possible to fit a sine wave under these conditions as a matter of interest.

Originally Posted by charlieahill

If anyone has any ideas, I'd still be interested to know whether it's possible to fit a sine wave under these conditions as a matter of interest.

Fitting a sine function y = Asin(Bx+C)+D to experimental data is a difficult problem. Of course only the points on the area of the sine wave have to be considered and the other points excluded. Since they are 4 parameters A, B, C, D to be optimized, the number of experimental points must be large enough.
A method is discribed in the paper "Régressions et équations intégrales" : JJacquelin's Documents | Scribd
(in French. No translation available today) which includes a chapter "Régression sinusoidale" : theory and application pp.21-34 and usable equations pp.35-36