[linux-audio-dev] jamin and FFT filtering

[Steve Harris]

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