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| -rw-r--r-- | Fourier Series.page | 5 |
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diff --git a/Fourier Series.page b/Fourier Series.page index b16663f..eceb1ca 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -68,12 +68,13 @@ It is easy to show that any product of cosines and sines can be expressed as the 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 - +<center> </center> 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. It turns out that the above function can be approximated as the sum of two cosines, namely, $\cos^{2n}(x) + cos^{2n+1}(x)$ -<center>  </center> +<center>  </center> +Summing these two ##What is the Fourier series actually?</b> |