need help understanding meaning of FFT

On Aug 8, 4:21&#4294967295;pm, julius <juli...@gmail.com> wrote:
> On Aug 8, 3:44&#4294967295;pm, ggk <ggkm...@comcast.net> wrote:
>
> > Thanks so much Kenn,
>
> > I think my first step here is to identify where the spur frequencies
> > are located, with high accuracy. Seems like your scheme above is the
> > perfect answer.
>
> > Best regards, -GGK
>
> The spectrum of a signal is defined as:
>
> &#4294967295;S_{xx}(f) = E[ | X(f) |^2 ]
>
> as Dirk suggested.

Thanks Julius, just so I'm clear... are you saying that it is always
more mathematically correct to average FFTs as root-sum-square because
the spectrum is defined as above?

On Aug 8, 6:29&#4294967295;pm, ggk <ggkm...@comcast.net> wrote:

>
> Thanks Julius, just so I'm clear... are you saying that it is always
> more mathematically correct to average FFTs as root-sum-square because
> the spectrum is defined as above?

It depends on what you are trying to do (and it sounds like you're
not sure).  If you want to estimate the spectrum of a signal, then
yes, average of magnitudes is the way to go.

I think that what you are asking can be answered by reading up
on "periodogram", "spectrum estimate", "Bartlett's method",
"Welch's method".

Roughly speaking, one trades off between noise reduction and
resolution.  The MATLAB docs are actually pretty decent expositions
targeted to the different methods implemented, such as pwelch,
bartlett, etc.