[SciPy-user] sine transformation weirdness
Lubos Vrbka
lists@vrbka....
Thu Jul 31 09:43:22 CDT 2008
hi guys,
while using the sine transformation from sandbox
http://projects.scipy.org/scipy/scipy/browser/trunk/scipy/sandbox/image/transforms.py
i encountered some confusion with respect to the constants involved in
the transformation process. to test it, i tried to do discrete sine
transformation of
f(r) = exp(-r)
analytically, the result is
f(k) = sqrt(2/pi) * k/(1+k^2)
for the discrete transformation i used dr=0.1, 1000 points, dk =
pi/(npoints*dr) since the dst uses effectively the double number of
sampling points. you can see the result in the attached file (hopefully
it gets it through). the blue line is the analytical result (without the
sqrt(2/pi) factor), green is the numerical discrete sine transform and
the red line is f(k,numerical)/f(k,analytical) ratio. in case the figure
doesn't make it through, the red line looks like one half of reverted
parabola. for r=0, its value is ~10. it reaches 0 at the distance
corresponding to the last sampling point.
apparently, there is some non-constant factor present here - i just
don't know what factor it might be. it has to come from the FFT used
inside the DST routine... i'd be very glad for any hint in this respect.
thanks in advance! with best regards,
lubos
--
Lubos _@_"
http://www.lubos.vrbka.net
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