ASN2 - Something Interesting: Exponential: Difference between revisions

Revision as of 07:43, 3 December 2009

Fourier Series

Using cosine to represent the basis functions $x (t) = \sum_{n = 0}^{\infty} a_{n} c o s (\frac{2 π m t}{T})$

Using an exponential to represent basis functions $x (t) = \sum_{n = 0}^{\infty} a_{n} e^{(} \frac{j 2 π m t}{T})$

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 Fourier Series
+Using cosine to represent the basis functions
 <math> x(t)= \sum_{n=0}^\infty a_n cos(\frac{ 2 \pi mt}{T}) \!</math>
- plot <math> \ \frac{2}{T} \sum_{n=1}^\infty sin\bigg(\frac{2 \pi nt}{T}\bigg) \!</math><br><br>
+Using an exponential to represent basis functions
+<math> x(t)= \sum_{n=0}^\infty a_n e^(\frac{ j2 \pi mt}{T}) \!</math>