Re: Why window in time domain before FFT?

On Nov 5, 11:22 am, Jerry Avins <j...@xxxxxxxx> wrote:
robert bristow-johnson wrote:
On Nov 4, 11:52 pm, Jerry Avins <j...@xxxxxxxx> wrote:
Richard Owlett wrote:
robert bristow-johnson wrote:
...
okay, Richard, then this is where the rubber meets the road regarding
this occasional little dispute that crops up here regarding the
alledged *inherent* periodic nature of the DFT (which is what the FFT
is an implementation of). i am a partisan in this debate that says
that the DFT *inherently* periodically extends the finite data passed
to it.
I think I agree with you. ...
I'm unsure of how much I'm on your side of the discussion as you didn't
give a summary of the opposing view.

oh, it's here on Google Groups archives somewhere (i don't wanna look
for it, there were at least 2 or 3 big ugly episodes). the other view
of the DFT is that it is (inherently?) the DTFT of the rectangularly
windowed signal (the rect window is length N and keeps x[0] to
x[N-1]), so it inherently windows the signal, even if you do not
(which results in a sinc convolved with the spectrum). the other
requirement of the other view of the DFT is that the output of that
DTFT is sampled at N equal frequencies from -Nyquist to +Nyquist, so
that at those sample points in the frequency domain, the sinc
convolution is not visible, but is visible *in between* the sample
points (whereas i say there ain't no in-between, unless we be talking
interpolation).

My way of looking at it is simple (like me) and I think it sidesteps a
lot of the finger pointing. Consider a periodic signal seen through a
rectangular window (the most common flat-topped kind!). Now construct
another signal that is identical to what shows through the window and is
zero everywhere else. Clearly, FFTs of these signals will produce the
same numbers. If someone wants to claim that they are nevertheless
somehow different -- different auras? -- be my guest.

they can only make that claim from some outside knowledge of the
nature of the audio being sampled as (possibly overlapping) sections
of N contiguous samples. if you know that it's full polyphonic,
reasonably broadbanded, then you can sorta assume the typical
sinusoidal component is not exactly an integer multiple of some common
fundamental in the audible range.

if it was nicely windowed before sending it to the DFT, then i would
think it wouldn't matter. you can pick out the components of a nice
harmonic note or you can pick out the components of a mix of sinusoids
of unrelated frequencies.


I'm working on a question about the rest of your post. But I can't quite
figure out what my question is.

wunnerful. looks like i dug another hole for myself.

You and your big shovel!

maybe if i lay low, i can slither out of it.

Keep in mind that no naturally occurring signals are truly periodic. A
single sustained organ note comes very close.

organ-schmorgan. just another synthesizer. :-)

I meant a pipe organ.

just another synthesizer. with mostly mechano-acoustic circuits.

When two notes are sounded, the result isn't
periodic because there won't be a common submultiple to the frequencies.

depends on the two notes. if they be fifths or octaves (or even
fourths or major thirds), there's gonna be a common submultiple. as
the interval of the two notes becomes less harmonic (or more
dissonant, where the frequency ratio between the two is a simplified
ratio of integers that are not small integers), this common
submultiple gets lower in frequency and eventually outside the range
of hearing tones (20Hz - ???).

there is no such thing as true DC either (i guess not, since DC is
periodic). sometime since our caveman days, we turned it on and
eventually we turn it off sometime before global warming or some other
cataclysm (like we lose the magnetic pole, which results in the loss
of the radiation belt that protects our atmosphere from solar wind,
and the sun blows it away like it did to Mars it's amazing what the so-
called "iron catastrophe" did 4 billion years ago to save our sorry
little asses) kills off the whole planet.

There's a transient when the switch closes, but you don't have to wait
long before nobody can tell. The other end is more interesting. I submit
that the only transient when the switch opens is due to arcing, if any.
Once the switch is open, there's no signal at all. What carries the
transient that mathematics demands? :-)

it's in-between the samples.

r b-j

.

Relevant Pages

  • Re: Why window in time domain before FFT?
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