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Engineering Tables/DFT Transform Properties
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Engineering Tables
The text in its current form is incomplete.
Periodic Sequence (Period N)
DFS Coefficients (Period N)
Notation
x
~
[
n
]
{\displaystyle {\tilde {x}}[n]}
x
~
[
k
]
{\displaystyle {\tilde {x}}[k]}
periodic with period N
Linearity
a
1
x
~
1
[
n
]
+
a
2
x
~
2
[
n
]
{\displaystyle a_{1}{\tilde {x}}_{1}[n]+a_{2}{\tilde {x}}_{2}[n]\ }
a
1
X
~
1
[
k
]
+
a
2
X
~
2
[
k
]
{\displaystyle a_{1}{\tilde {X}}_{1}[k]+a_{2}{\tilde {X}}_{2}[k]\ }
X
~
[
n
]
{\displaystyle {\tilde {X}}[n]}
N
x
~
[
−
k
]
{\displaystyle N{\tilde {x}}[-k]}
Time shifting
x
~
[
n
−
m
]
{\displaystyle {\tilde {x}}[n-m]\ }
W
N
k
m
X
~
[
k
]
{\displaystyle W_{N}^{km}{\tilde {X}}[k]\ }