# Fourier analysis

#### hanson

Hi all.
I am learning a numerical method that involves Fourier transform.
As far as I know, I think Fourier transform is tool to find the frequency spectrum of a signal.
And the usual form shall be
"Integrate from negtive infinity to positive infinity, f(x)*exp(i*w*x)dx"

However, when i search this in wikipedia, it is defined with (w-wo), where wo is the central frequency.

http://en.wikipedia.org/wiki/Split-step_method

I don't really know what this definition is doing and what changes it would bring.

Why is it necessary to do so?

#### fresh_42

Mentor
2018 Award
Second, it is necessary to Fourier transform back and forth because the linear step is made in the frequency domain while the nonlinear step is made in the time domain. An example of usage of this method is in the field of light pulse propagation in optical fibers, where the interaction of linear and nonlinear mechanisms makes it difficult to find general analytical solutions. However, the split-step method provides a numerical solution to the problem.

"Fourier analysis"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving