Fourier Series: Small Waves & Equal Amplitude

[Emilijo]

In Fourier series we have small waves on the top of big waves (the function seems like that),
but the small waves do not have the same amplitude. Does somebody know how to get a function with waves and small waves on the top but with the same amplitude.

 

[Office_Shredder]

What is the definition of a small wave if it doesn't have anything to do with amplitude?

 

[Emilijo]

Can you see now, small waves on the top of big wave are not the same (equal amplitude)
{click on the picture to see it better}

 

[S_Happens]

If you're talking about the changing amplitude of the Fourier Series approximation then the answer is that you really can't. Due to the Gibbs Phenomenon, you'll have an overshoot at any discontinuity, of which the amplitude doesn't diminish.

 

[Emilijo]

Do you know how to get a function (any kind of function) with "small" waves on the top of "big" waves, but for the same amplitude of all small waves?

 

[Office_Shredder]

Is small referring to the wavelength of the wave? Just take something like cos(x)+cos(100x)
http://www.wolframalpha.com/input/?i=cos(x)+cos(100x)

Why would you want such a thing?

 

[Emilijo]

I mean something like that:
View attachment Scanned at 3.4.2012 19-58.pdf

Can you get a function something like that?
(rotate the picture)

 

[HallsofIvy]

The Fourier series is of the form
\sum A_n cos(nx)+ B_n sin(nx)

It looks to me like your series happens to have only two non-zero terms, one with a period of about 6 and amplitude 3000, the other with period about .6 and amplitude about 100. In other words, something like
3000 cos(2\pi x/60)+ 100 cos(10(2\pi/60))

 

[Emilijo]

The Fourier series is of the form
\sum A_n cos(nx)+ B_n sin(nx)

It looks to me like your series happens to have only two non-zero terms, one with a period of about 6 and amplitude 3000, the other with period about .6 and amplitude about 100. In other words, something like
3000 cos(2\pi x/60)+ 100 cos(10(2\pi/60))

-Your function is not like on the atachment,
do you have better idea?

 

[Office_Shredder]

The 60s should be 6s to get a period of 6 (although changing the period of both won't change the local structure), and he forgot an x in the second cosine

Here's the re-worked version graphed in wolfram alpha
http://www.wolframalpha.com/input/?i=3000cos(2πx/6)+100cos(10(2πx/6))+from+x=0+to+x=12

 

[Emilijo]

I found a function: sin(1-cos(x))
But there are only 2 "small" waves on every wave (put the function in wolfram)
How to get 3, 4, 5, ... or n "small" waves?