additive

[Rowena Larkins]

> But there is the other side as well:  Does the above mentioned method
> of FFTing with no window function make sense in the meaning of spectral
> content ? I'd say no! Chopping the signal into window chunks creates
> (artificial) discontinuities, if you treat a long sine wave sample,
> you'll get very strange "spectra", this is clear , because after
> chopping the signal is no sine wave any more. If you wan't to have a
> meaningfull spectral representation, you'll have to apply a window
> function w(t), and this means convolution with the spectral equivalent
> W(s), ie. smearing.  This smearing or unsharpness will hide the little
> dirty "harmonics", that makes the sound of instruments so interesting.
> 
> Does this remind you of something? It is the Heisenberg theorem applied
> to music instead of quantum physics (the math is the same in this
> case):  time resolution rivals with spectral resolution. If you want
> good spectral resolution, the window has to be very long, thus time
> resolution suffers and vice versa.

> 



Given that both are dealing with wave theory, then this is not really suprising.


Rowena