Re: Wanting to take a FFT transform of a irregularly spaced sample

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On Mon, May 16, 2022 at 7:57 AM ashwin .D <[email protected]> wrote:

> Robert,
>                 When you write "you may want to reduce the number of
> points you sample at first for visualization, then you can zoom in at the
> full frequency resolution to an area of interest if there is lots of dead
> space." are you referring to the
> https://en.wikipedia.org/wiki/Welch%27s_method and implemented by
> https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.welch.html
> ? This provides for  an efficient noise reduction .
>

No, I just meant that you get to pick the array of frequencies that the
periodogram is sampled on. You can pick anything (that doesn't include
f=0), so you could start with a coarse sampling to see where the major
frequency content is. Then if the frequency content is constrained to one
region, then you can choose a finer sampling of frequencies only within
that band. That can save on computation costs if it's too expensive to do a
fine sampling over the whole Nyquist range. But if it's cheap enough to do
the fine sampling over the whole region, go ahead and do that.

I don't know of any work that apply's something like Welch's method per se
to the LS periodogram, but if you squint, you can kind of see Welch's
method as an ad hoc instance of a multitaper method, and there is a more
rigorous application of multitaper methods to the LS periodogram. Not
implemented in Python so far as I know, but there is an R implementation.

  https://iopscience.iop.org/article/10.3847/1538-3881/ab7fa1

-- 
Robert Kern

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<div dir=3D"ltr"><div dir=3D"ltr">On Mon, May 16, 2022 at 7:57 AM ashwin .D=
 &lt;<a href=3D"mailto:[email protected]">[email protected]</a>&gt; wrote=
:<br></div><div class=3D"gmail_quote"><blockquote class=3D"gmail_quote" sty=
le=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);paddi=
ng-left:1ex"><div dir=3D"ltr">Robert,<div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 When you write &quot;you may want to reduce the nu=
mber of points you sample at first for visualization, then you can zoom in =
at the full frequency resolution to an area of interest if there is lots of=
 dead space.&quot; are you referring to the=C2=A0<a href=3D"https://en.wiki=
pedia.org/wiki/Welch%27s_method" target=3D"_blank">https://en.wikipedia.org=
/wiki/Welch%27s_method</a> and implemented by=C2=A0<a href=3D"https://docs.=
scipy.org/doc/scipy/reference/generated/scipy.signal.welch.html" target=3D"=
_blank">https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.w=
elch.html</a>=C2=A0 ? This provides for=C2=A0 an efficient noise reduction =
.=C2=A0</div></div></blockquote></div><div><br></div><div>No, I just meant =
that you get to pick the array of frequencies that the periodogram is sampl=
ed on. You can pick anything (that doesn&#39;t include f=3D0), so you could=
 start with a coarse sampling to see where the major frequency content is. =
Then if the frequency content is constrained to one region, then you can ch=
oose a finer sampling of frequencies only within that band. That can save o=
n computation costs if it&#39;s too expensive to do a fine sampling over th=
e whole Nyquist range. But if it&#39;s cheap enough to do the fine sampling=
 over the whole region, go ahead and do that.</div><div><br></div><div>I do=
n&#39;t know of any work that apply&#39;s something like Welch&#39;s method=
 per se to the LS periodogram, but if you squint, you can kind of see Welch=
&#39;s method as an ad hoc instance of a multitaper method, and there is a =
more rigorous application of multitaper methods to the LS periodogram. Not =
implemented in Python so far as I know, but there is an R implementation.</=
div><div><br></div><div>=C2=A0 <a href=3D"https://iopscience.iop.org/articl=
e/10.3847/1538-3881/ab7fa1">https://iopscience.iop.org/article/10.3847/1538=
-3881/ab7fa1</a>=C2=A0</div><div><br></div>-- <br><div dir=3D"ltr" class=3D=
"gmail_signature">Robert Kern</div></div>

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