Re: Large FFT vs Many FFTs

On 8 Apr, 03:26, "dbd" <d...@xxxxxxxx> wrote:
On Apr 7, 4:00 pm, "Rune Allnor" <all...@xxxxxxxxxxxx> wrote:





On 8 Apr, 00:01, Randy Yates <y...@xxxxxxxx> wrote:

"Rune Allnor" <all...@xxxxxxxxxxxx> writes:
[...]
On 5 Apr, 12:44, "Edison" <bell...@xxxxxxxxxxxxxx> wrote:

The requirements state that the resulting very narrow bin width
will reduce the effect of noise.
[...]
Note that Var(P[k]) does *not* depend on the number of
samples N, meaning that the argument that "a large data
sequence reduces noise" is plain wrong.

Perhaps he meant that, for a given noise power spectral density, a
smaller bin width reduces the input noise power in that bin, which is
true.

The correctness of his statement depends on whether the "noise" he
mentioned is input noise or estimation noise (i.e., the variance you
were speaking of).

The statement "reduce the effect of noise" implies to me that
one expects a lower variance in the estimated periodogram.

Whatever was intended, the OP ought to be aware that the
periodogram is a notoriosly poor estimator for the PSD.

Rune

The expression:

Var(P[k]) = P[k]^2.

is true for bins containing Gaussian noise. It is not true for bins
containing a tone with energy considerably greater than the noise
energy in the bin. The OP has a task of measuring a base frequency
component and harmonic components, not measuring noise.

In the applications I have encountered in the past where
"harmonic distrortion" has been an issue, the energy
contained in the harmonics have been on the order of
1% - 3% of the total power. The OP is tasked with measuring
the 5th harmonic, indicating to me that he is well into
the area where the energy of the harmonics are no longer
"greater than the noise energy in the bin."

In other words, the task is very likely to decide "is this
really an harmonic or is it a spurious noise peak?"

By the way, the internet has made a change in book availability. The
'old books' are often available used a reasonable cost. I just picked
up a copy of Tukey and Blackman's Dover printing of "The Measurement
of Power Spectra" for under $10. That's a lot more than the $1.85
price in 1959 but still less than current texbook prices.

Almost half the books in my bookshelf are Dovers. The problem
is the books that presently are out of print (like Kay's 1988 book
or Scharf's 1991 book) which have not yet become re-published
by Dover.

Rune

.

Relevant Pages

  • Re: Analysis of gas mode MM interferometer operation using standard SR formulae.
    ... Michelson and Morley 1887 Experiment and the Discovery of Absolute ... Hence your complaint about a "deficit" in this bin is ... If there is a lack of "noise" in bin 20, ... matched by an equal value at the opposite marker. ...
    (sci.physics.relativity)
  • Re: Large FFT vs Many FFTs
    ... sequence reduces noise" is plain wrong. ... smaller bin width reduces the input noise power in that bin, ... The OP has a task of measuring a base frequency ... component and harmonic components, not measuring noise. ...
    (comp.dsp)
  • Re: Many brands doing NR post-sensor on raw files at high ISO??
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    (rec.photo.digital.slr-systems)
  • Re: question for JA, 3-4-07
    ... noise can be as much as 130dB (FFT bin level) down from ... More points in the FFT, lower bin levels, ... on the same noise data. ...
    (rec.audio.opinion)
  • Re: Pristine Audio XR - doubling the frequency range of 78s
    ... Now it's safe to assume that these were not brick-wall filters, but that they rolled off the upper frequencies smoothly up the range, with those upper harmonics gradually disappearing into the background noise. ... I have a later recording I'm currently working on which indicates a sharper roll-off curve was used than in that 1929 Kreuzter recording, and I'm only seeing harmonics up to about 12.5kHz. ...
    (rec.music.classical.recordings)
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