# [SciPy-user] sine transform prefactor

Lubos Vrbka lists@vrbka....
Sat Jul 26 09:43:13 CDT 2008

hi guys,

since i am not a mathematician, i'd like to ask one question related to
discrete sine transform and its implementation in scipy (sandbox at the
moment).

from definition, the continuous sine transform comes with the constant
prefactor of sqrt(2/pi), i.e.,

FST(f(r)) = f(k) = sqrt(2/pi) int_0^{\infty} f(r) sin(kr) dr
iFST(f(k)) = f(r) = sqrt(2/pi) int_0^{\infty} f(k) sin(kr) dk

how is it in case of a discrete transform? does this sqrt(2/pi) factor
come into play also for discrete transforms, or is it applicable only
for continuous transforms? if it is applicable, is it already included
inside the routines? how is it then distributed among the forward and
reverse transform?

i think the situation here might be complicated by the fact, that the
code in sandbox uses the fast fourier transform for the evaluation of
the sine transform - and this might probably change the constants
involved as well (since the fourier transform should be 'normalized'
with a factor of 1/2pi).

i would be very grateful for any help on this issue. my program seems to
run, but it is dependent on the choice of the constant factors involved
in the transforms. so far i've found the correct combination (it seems
so), but i'd like to make this more rigorous and to really understand _why_.

thanks a lot in advance. best,

--
Lubos _@_"
http://www.lubos.vrbka.net