What math function could fit this curve

[Glenn]

Friends:

I have 2 shapes and I would like to fit a curve to them such that I can recreate the shapes knowing the amplitude and wavelength. They look sinusoidal to some extent. I have enclosed a png. The top 2 shapes are a wave like you might find on water. The second has double the wavelength of the first. The 3rd is more like a drop falling or metal bending. The 4th is the same thing with double the wavelength. Any ideas?

[jpdrolet]

It looks like a bell shape (gaussian, lorentzian) mutiplied by a polynom or a sine/cosine function. If these are waves produced by a drop, then it might be Bessel functions (wave solutions of an oscillating membrane).

[gammalight]

The first two look similar to an arctan type function, multiplied by some quartic. I agree with jpdrolet the second two look Gaussian or Lorentzian in shape, but also look like the sinc function with quickly decaying ripples trailing off each tail.

[Dirk J.]

I guess you need to find out what your curves represent and not what they look like.

My guess: top one is some kind of absorption peak (Gaussian/Lorenzian) and the second one is related through it by a Kramers-Kronig relation or something similar. You can estimate it roughly by the derivative of a Gaussian.

QUOTE(Glenn @ May 22 2007, 10:24 PM)

They look sinusoidal to some extent.

[Glenn]

I think I'll try looking at the frequency spectrum (Fourier).

Thanks everyone.