On Wed, Aug 11, 2004 at 03:53:09 +0200, Alfons Adriaensen wrote:
In general it will not. Consider a simple case: your
signal is a cosine
wave with n periods in the FFT length and amplitude 1. When you apply
the raised cosine window, what happens is that two new cosines with
resp. n-1 and n+1 periods per FFT length and amplitude -0.5 are added,
giving of course zero at both ends.
The same happens with a more complex signal: the amplitudes of all cosine
components are modified so as to make them cancel at the ends. When you
disturb that delicate balance, they will no longer cancel out.
Now for each group of three adjacent bins, a linear g(f) slope will not
modify the sum of the ampitudes, e.g. it could transform the -0.5, 1,
-0.5 of above into -0.6 1 -0.4, but the sum is still zero. So the
inbalance and the expected signal amplitude at the ends after the IFFT
will be proportional to the second derivative of the frequency response.
OK, thanks, I think I followed that, but I need to think on it harder.
BTW, before you mentioned root raised consine windows before and after, I
did a bit of googling, and couldn't find much reference to root raised cos
in windowing (just pentions in-passing), do you have a reference or
the windowing function/attentuaion factor or anything?
In the meantime I'l try it with vanilla raised cosines.
- Steve