The Fourier transform exists if is Lebesgue integrable on the whole real axis.
Sometimes the Fourier transform is also defined without the factor in one direction, but therefore giving the transform into the other direction a factor . So when looking a transform up in a table you should find out how it is defined in that table.
where and are constants.
We define the bilateral convolution of two functions and as:
Then the following equation holds:
If is some signal (maybe a wave) then the frequency domain of is given as . Rayleigh’s theorem states that then the energy carried by the signal given by:
can also be expressed as:
In general we have:
also known as the first Parseval theorem.
|Date of creation||2013-03-22 12:34:28|
|Last modified on||2013-03-22 12:34:28|
|Last modified by||mathwizard (128)|
|Defines||first Parseval theorem|