From 7dce994acfa2abc53ac586be143dc815f37c1a6a Mon Sep 17 00:00:00 2001 From: siveshs Date: Fri, 2 Jul 2010 19:47:21 +0000 Subject: section 2 editing --- Fourier Series.page | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/Fourier Series.page b/Fourier Series.page index 8ac7870..40411b5 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -66,9 +66,10 @@ $$ It is easy to show that any product of cosines and sines can be expressed as the product of exponentials which will reduce to a sum of sines and cosines. -As a final test to see if the Fourier series really could exist for any periodic function, we consider a periodic function with a sharp peak as shown below ---- Image goes here --- - +As a final test to see if the Fourier series really could exist for any periodic function, we consider a periodic function with a sharp peak as shown below + +![Peak Function Image](/peak_func.gif) + If it is possible to approximate the above function using a sum of sines and cosines, then it can be argued that *any* continuous periodic function can be expressed in a similar way. This is because any function could be expressed as a number of peaks at every position. -- cgit v1.2.3