|
Signal |
Fourier transform unitary, angular frequency |
Fourier transform unitary, ordinary frequency |
Remarks
|
|
|
|
|
|
1
|
|
|
|
Linearity
|
2
|
|
|
|
Shift in time domain
|
3
|
|
|
|
Shift in frequency domain, dual of 2
|
4
|
|
|
|
If is large, then is concentrated around 0 and spreads out and flattens
|
5
|
|
|
|
Duality property of the Fourier transform. Results from swapping "dummy" variables of and .
|
6
|
|
|
|
Generalized derivative property of the Fourier transform
|
7
|
|
|
|
This is the dual to 6
|
8
|
|
|
|
denotes the convolution of and — this rule is the convolution theorem
|
9
|
|
|
|
This is the dual of 8
|
10
|
For a purely real even function
|
is a purely real even function
|
is a purely real even function
|
11
|
For a purely real odd function
|
is a purely imaginary odd function
|
is a purely imaginary odd function
|