The function is even and continuous, with period . On it is , so it rises from zero to one at , crosses zero at , reaches minus one at , and returns to zero at . Reflect this curve about the vertical axis and repeat periodically. The joins at integer multiples of have corners, but no jumps.
Figure 1.
Even periodic extension of a sine mode and its Fourier approximation
. Original plot over two periods. The dashed approximation uses the first twelve nonzero cosine coefficients; the exact function is continuous with corners at integer multiples of . Details.

Ancestors (13)

  1. a
  2. 11
  3. Paper 1
  4. 2006
  5. Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
  6. Mathematics course of the year 1 of the natural sciences course of the University of Cambridge
  7. Year 1 of the natural sciences course of the University of Cambridge
  8. Year of the natural sciences course of the University of Cambridge
  9. Natural sciences course of the University of Cambridge
  10. Course of the University of Cambridge
  11. University of Cambridge
  12. List of universities
  13. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version