Fourier series and transforms

  • Thread starter rakeshbs
  • Start date
17
0
Fourier series is a way to express a periodic function as a sum of complex exponentials or sines and cosines.. Is there actually a proof for the fact tat a periodic function can be split up into sines and cosines or complex exponentials?
 

HallsofIvy

Science Advisor
Homework Helper
41,715
876
It is fairly easy to show that any integrable periodic function can be approximated arbitrarily well by a sum of sines and cosines. The Fourier series is the limit of those approximations as the "error" goes to 0- except on a set of measure 0 for dis-continuous functions. I might point out that the other way is what's hard. It can be shown that some perfectly valid Fourier series converge to non-(Riemann)-integrable functions. That was why Lebesque integration had to be invented.
 

Related Threads for: Fourier series and transforms

Replies
1
Views
606
Replies
1
Views
957
Replies
1
Views
2K
  • Posted
Replies
3
Views
1K
Replies
1
Views
2K
  • Posted
Replies
7
Views
694
  • Posted
Replies
2
Views
1K

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

Hot Threads

Top