| Line 2: | Line 2: | ||
| − | 8 + sin<math>( \frac{2 pi n}{N} )</math> + 8cos<math>( \frac{4 pi n}{N} )</math> | + | 8 + sin<math>( \frac{2 pi n}{N} )</math> + 8cos<math>( \frac{4 pi n}{N} )</math> |
| − | = 8 + <math>( \frac{1}{2j})</math> { e^(<math>( \frac{j2 pi n}{N} )</math>) - e^(<math>( \frac{-j2 pi n}{N} )</math> } + 8 { e^(<math>( \frac{j4 pi n}{N} )</math>) - e^(<math>( \frac{-j4 pi n}{N} )</math> } | + | = 8 + <math>( \frac{1}{2j})</math> { e^(<math>( \frac{j2 pi n}{N} )</math>) - e^(<math>( \frac{-j2 pi n}{N} )</math> } + 8 { e^(<math>( \frac{j4 pi n}{N} )</math>) - e^(<math>( \frac{-j4 pi n}{N} )</math> } |
| − | = 8 + <math>( \frac{-1j}{2})</math> { e^(<math>( \frac{j2 pi n}{N} )</math>)} + <math>( \frac{1j}{2})</math> { e^(<math>( \frac{-j2 pi n}{N} )</math>)} +4 { e^(<math>( \frac{j4 pi n}{N} )</math>)} +4 { e^(<math>( \frac{-j4 pi n}{N} )</math>)} | + | = 8 + <math>( \frac{-1j}{2})</math> { e^(<math>( \frac{j2 pi n}{N} )</math>)} + <math>( \frac{1j}{2})</math> { e^(<math>( \frac{-j2 pi n}{N} )</math>)} +4 { e^(<math>( \frac{j4 pi n}{N} )</math>)} +4 { e^(<math>( \frac{-j4 pi n}{N} )</math>)} |
Therfore, we have te coeffients as | Therfore, we have te coeffients as | ||
<math>a_0</math> = 8 | <math>a_0</math> = 8 | ||
Revision as of 17:50, 26 September 2008
Let the DT siganl be
8 + sin$ ( \frac{2 pi n}{N} ) $ + 8cos$ ( \frac{4 pi n}{N} ) $
= 8 + $ ( \frac{1}{2j}) $ { e^($ ( \frac{j2 pi n}{N} ) $) - e^($ ( \frac{-j2 pi n}{N} ) $ } + 8 { e^($ ( \frac{j4 pi n}{N} ) $) - e^($ ( \frac{-j4 pi n}{N} ) $ }
= 8 + $ ( \frac{-1j}{2}) $ { e^($ ( \frac{j2 pi n}{N} ) $)} + $ ( \frac{1j}{2}) $ { e^($ ( \frac{-j2 pi n}{N} ) $)} +4 { e^($ ( \frac{j4 pi n}{N} ) $)} +4 { e^($ ( \frac{-j4 pi n}{N} ) $)}
Therfore, we have te coeffients as
$ a_0 $ = 8
