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| -rw-r--r-- | Fourier Series.page | 6 |
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diff --git a/Fourier Series.page b/Fourier Series.page index e01fec9..9df0960 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -66,6 +66,12 @@ $$ 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 --- + +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. + + ##What is the Fourier series actually?</b> ##Why is Fourier series useful? </b> |