Engineering Tables/DFT Transform Properties
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| Periodic Sequence (Period N) | DFS Coefficients (Period N) | |
|---|---|---|
| Notation | periodic with period N | |
| Linearity | ||
| Time shifting |
![{\displaystyle {\tilde {x}}[n]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f0b944d1740999c970befbae73c94687b80ee69)
![{\displaystyle {\tilde {x}}[k]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1d70999df78f4c5ae1ab5f01a2529682ea0ed9e)
![{\displaystyle a_{1}{\tilde {x}}_{1}[n]+a_{2}{\tilde {x}}_{2}[n]\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/74eed87b4ca8016708411db0728e6df95567b260)
![{\displaystyle a_{1}{\tilde {X}}_{1}[k]+a_{2}{\tilde {X}}_{2}[k]\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/260708cd2ecb8c87cbded6b32e6a46395e8a3f55)
![{\displaystyle {\tilde {X}}[n]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff86b7ce372b688047f5848327f824943ca9bbd6)
![{\displaystyle N{\tilde {x}}[-k]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a152ba499a8ea7317c4ea64804b79142c3a3d38)
![{\displaystyle {\tilde {x}}[n-m]\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ff891c9cc75052409ca4e88f91e1b1babb881fb)
![{\displaystyle W_{N}^{km}{\tilde {X}}[k]\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2441bb8ddb518483d91c7c5d78973a4640bc744e)