approaching infinity

[AntonioLao]

Mathematical logic says that a periodic function can be expanded by using Fourier series as a sum of discrete components of trigonometric sine and cosine terms. However, if and only if the period approaches infinty can its transform pairs exist. http://en.wikipedia.org/wiki/Fast_Fourier_transform and http://mathworld.wolfram.com/FourierTransform.html

[harmonygirl]

Antonio,
This is over my head. Can you explain what it means?

[mkirkpatrick]

Mathematical logic says that a periodic function can be expanded by using Fourier series as a sum of discrete components of trigonometric sine and cosine terms. However, if and only if the period approaches infinty can its transform pairs exist. http://en.wikipedia.org/wiki/Fast_Fourier_transform and http://mathworld.wolfram.com/FourierTransform.html

An idea has
arose in my mind here Antonio,approaching infinity,and thereby entering an
ubiquitous field,you would be in the "border land" between on,and off?Motion
would meet its Doppleganger motionlessness!Ultra fast would meet ultra slow
and would in effect cancel each other out!The transform pairs you mention
are I believe sub atomic vortices.Maybe you could dig out a equation from
here Antonio,that could be used on the key to the TOE thread.!

kind regards michael.

[AntonioLao]

This is over my head. Can you explain what it means?

Using a biological analogy, the transform pairs are just like male and female. Both are needed for further propagation of the species in question. In wave propagation there are also pairs of positive and negative waves.

Maybe you could dig out a equation from here

The wave equation of classical electromagnetic field has been quite successful when applied to quantum mechanics http://en.wikipedia.org/wiki/Wave_equation and http://www.geocities.com/aboutwaves/

[harmonygirl]

Positive and negative waves? I fell through the looking glass on that one. Are these negative and positive in relation to each other or to another frame of reference? So in your first post, are you saying that these 'pairs' only exist once the period approaches infinity?

[AntonioLao]

Are these negative and positive in relation to each other or to another frame of reference?

Here again, I am having problem finding the proper terminology for describing positive and negative frequency. The best analogy is clockwise and counterclockwise rotations. http://en.wikipedia.org/wiki/Fourier_transform and http://en.wikipedia.org/wiki/Spatial_frequency and http://en.wikipedia.org/wiki/Wave_number and http://en.wikipedia.org/wiki/Angular_frequency and http://en.wikipedia.org/wiki/Frequency