# Thread: Develop Model Emulating Given Wave Pattern

1. ## Develop Model Emulating Given Wave Pattern

Question:
Develop a model for producing a repeating pattern of 8 waves, with 6 smaller waves of approx. the same size and the second and sixth waves much larger. The sketch below gives a general indication of the eight wave pattern.

(Sorry for large image)

I would like to know how to "take a shot" at it, the solution must be a sine function. Can be generic, by that I mean no definite amplitude, only that the model clearly resemble the one given.

I have tried to emulate it by trial and error, combining functions such as in the form [y=sin x + 0.3sin3x] with no luck.

-Ausmate

2. ## Re: Develop Model Emulating Given Wave Pattern

Originally Posted by ausmate
Question:
Develop a model for producing a repeating pattern of 8 waves, with 6 smaller waves of approx. the same size and the second and sixth waves much larger. The sketch below gives a general indication of the eight wave pattern.

(Sorry for large image)

I would like to know how to "take a shot" at it, the solution must be a sine function. Can be generic, by that I mean no definite amplitude, only that the model clearly resemble the one given.

I have tried to emulate it by trial and error, combining functions such as in the form [y=sin x + 0.3sin3x] with no luck.

-Ausmate
I don't have a complete answer for you, but I think that adding the functions is going to be harder to do than multiplying. For example:

I can't manage three "humps" between the large ones, though. You can, of course, do this using Fourier analysis, but it would involve a large number of terms.

-Dan

3. ## Re: Develop Model Emulating Given Wave Pattern

Thanks for the answer Dan, but I think I am required to add sine functions to get the desired pattern, any ideas on how to start?

-ausmate

4. ## Re: Develop Model Emulating Given Wave Pattern

My general approach would be as follows.

For the small humps, I'd take a simple sine function of frequency $\displaystyle \nu$.

For the large humps, I'd start with a more complicated function which is of frequency $\displaystyle \frac \nu 4$ which will basically consist of just the top half of a single sine wave, being zero everywhere else.

Then I would do a Fourier analysis on the latter, which ought to be more-or-less tractable, in a similar way to how it works for the half-wave rectified sine.

Then you add this to the raw sine function of frequency $\displaystyle \nu$.

I haven't tried it out, but it's an approach that may work for you.