Window function

On Sat, 10 Apr 2004 17:16:24 -0400, Jerry Avins <jya@ieee.org> wrote:

>Don't ask me to prove it, but windows, in effect, smear the smearing. In
>exchange for reducing the smearing if off-center frequencies, they add
>some to the centered ones. The best a good window can do is equalize
>smearing and confine it to near-by bins. It's that no-free-lunch thing.
>
>Jerry
>-- 

(snipped)

Yep, non-rectangular windows smear the spectral energy, 
that's centered right on a DFT bin, to neighboring bins.
When spectral energy is centered right on a DFT bin,
there will be no DFT leakage with rectangular windowing.
In that case windowing with a non-rectangular window 
is not a good idea.

If you take the Fourier transform of a Hann (also known 
as Hanning, von Hann, raised cosine) function, 
you'll get the sum of three sin(x)/x spectral 
components.  There will be sin(x)/x-shaped 
spectral energy centered at DC (0 Hz), a sin(x)/x 
centered at a positive freq, 
and a sin(x)/x centered at a negative frequency. 

[-Rick-]