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Discrete time Fourier series
 
Discrete time Fourier series
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<math>x[n] = \sum_{k=N} a_ke^{-jkw_0n}</math>
  
 
<math>a_k = \frac{1}{N}\sum_{n=N} x[n]e^{-jkw_0n}</math>
 
<math>a_k = \frac{1}{N}\sum_{n=N} x[n]e^{-jkw_0n}</math>

Revision as of 17:18, 25 September 2008

Discrete time Fourier series

$ x[n] = \sum_{k=N} a_ke^{-jkw_0n} $

$ a_k = \frac{1}{N}\sum_{n=N} x[n]e^{-jkw_0n} $

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett