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==Fourier Series Coefficients== | ==Fourier Series Coefficients== | ||
<math>a_{k} = \frac{1}{N} \sum_{n=0}^{N-1} x[n] e^{-jk \frac{2 \pi}{N} n}</math> | <math>a_{k} = \frac{1}{N} \sum_{n=0}^{N-1} x[n] e^{-jk \frac{2 \pi}{N} n}</math> | ||
| + | |||
| + | From the plot above, N = 4: | ||
| + | |||
| + | <math>a_{k} = \frac{1}{4} \sum_{n=0}^{3} x[n] e^{-jk \frac{2 \pi}{4} n}</math> | ||
Revision as of 16:29, 23 September 2008
Periodic DT Signal
The following plot shows two periods of the periodic DT signal $ x[n] $, a sawtooth:
Fourier Series Coefficients
$ a_{k} = \frac{1}{N} \sum_{n=0}^{N-1} x[n] e^{-jk \frac{2 \pi}{N} n} $
From the plot above, N = 4:
$ a_{k} = \frac{1}{4} \sum_{n=0}^{3} x[n] e^{-jk \frac{2 \pi}{4} n} $
