Engineering Tables/Fourier Transform Properties
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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 |