The properties of the Fourier transform are important in applying it to signal
analysis and to interpreting it. The main properties are given here using thenotation that the FT of a real valued function
over all time
is given by
.
- Linear:
- Even and Oddness: if
and
then
even
0even
0even
0odd
00
oddeven
00
even0
eveneven
0
oddodd
0even
- Convolution: If continuous convolution is definedby:
then
- Multiplication:
- Parseval:
- Shift:
- Modulate:
- Derivative:
- Stretch:
- Orthogonality: