The finite Fourier cosine transform of an apodization function, also known as an
apparatus function. The instrument function 
corresponding to a given apodization
function 
is
 |
(1)
|
which, upon expanding the complex exponential,
 |  |  |
(2)
|
 |  |  |
(3)
|
For 
an even function, the left integrand
is even (and hence is equal to twice its value over half its interval) and the right
integrand is odd (and hence equal to 0), so
 |
(4)
|
