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| -rw-r--r-- | Fourier Series.page | 7 |
1 files 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 + + + 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. |