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| author | siveshs <siveshs@gmail.com> | 2010-07-02 20:18:29 +0000 |
|---|---|---|
| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-07-02 20:18:29 +0000 |
| commit | dfa84415288afae1f072229b074e6de926b82915 (patch) | |
| tree | 49deb77c4245176e4cf237582d296e61938847f0 /Fourier Series.page | |
| parent | 9646e2dcec01e75985e3ecad43e1739245a19def (diff) | |
| download | afterklein-wiki-dfa84415288afae1f072229b074e6de926b82915.tar.gz afterklein-wiki-dfa84415288afae1f072229b074e6de926b82915.zip | |
section 2 editing
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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> |