Fourier Intergrals and transforms

Brewer

How do I do a Fourier integral (and whats the point of them??)

$$F(\omega) = \frac{1}{\sqrt{2\pi}}\int dte^{-\alpha t}cos\omega t$$

and I've not the foggiest idea what to do. I thought I could just go about doing in the integral by parts (limits are 0 and infinity by the way), but on further research I don't think I can do that can I?

d_leet

Try integration by parts.

mathman

cos(u)=(exp(iu)+exp(-iu))/2

Substitute into your integral and you will have the sum of two exp integrals. I presume you can do that.

Brewer

Yes thats familliar. I have done this integral before - just never dawned on me to use the substitution.

I was also a little confused when it called it a Fourier Integral. I thought it was going to be a lot more complex than it appears to be now.

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