[SciPy-user] sine transform prefactor

[Lubos Vrbka]

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 _ at _"
http://www.lubos.vrbka.net