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| -rw-r--r-- | Fourier Series.page | 4 |
1 files changed, 3 insertions, 1 deletions
diff --git a/Fourier Series.page b/Fourier Series.page index 1bd52f4..8010928 100644 --- a/Fourier Series.page +++ b/Fourier Series.page @@ -12,7 +12,9 @@ We first begin with a few basic identities on the size of sets. Then, we will sh --> don't have the notes for this ## Proof that no. of available functions is greater than number of functions required to define the periodic function ---> don't have the notes for this +Consider any arbitrary periodic function in the interval $[-\pi,\pi]$. This can be represented as a series of values at various points in the interval. For example, +$ f(0) = ... , f(0.1) = ..., f(0.2) = ... $ and so on. At each point, we can assign any real number (i.e. $\in \mathbb R$). So, the number of possible periodic functions in an interval is of the order of $\mathbb R^{\mathbb R}$. +--> don't quite remember how this goes. #<b>Why Fourier decomposition is plausible?</b> To show that Fourier series is plausible, let us consider some arbitrary trignometric functions and see if it is possible to express them as the sum of sines and cosines: |