Re: Sharpening oversampled STFT-based spectrograms

Michel

I think it will be clearer to respond in a altered order beginning
with you conclusion:

On Dec 28, 12:37 pm, Michel Rouzic <Michel0...@xxxxxxxx> wrote:

I'm talking about theory here, not implementation. But I won't hold it
against you either, it seems like it's a custom around here to ponder
practicality and feasibility before establishing the theoretical
possibility of something.

We discuss things here that fall into at least four categories:
Group 1
Theoretical limits of infinite and continuous extent
Group 2
Theoretical limits of finite and sampled extent
Group 3
Limits of
signal environment, noise, interference
robustness
algorithm choice
Group 4
coefficient generation method complexity
is there enough RAM
is the CPU fast enough
etc.

The inexperienced here often combine group2 with group3 and group4 as
'implementation details'. However both group2 and group1 are
theoretical. Group 3 might be 'feasibility' and Group 4 might be
'practicality'.

It's a custom around here to consider the theoretical requirements of
group 2 even with those unaccustomed to applying them, whether the
unaccustomed are aware of their nature or not.

dbd wrote:
On Dec 28, 5:38 am, Michel Rouzic <Michel0...@xxxxxxxx> wrote:

....
Oh I'm not talking about the 1D signal not being aliased but its
spectrogram not being aliased. Because when we get a spectrogram using
a STFT we "decimate" (by taking chunks spaced by N samples) therefore
we get aliased spectrograms.
'spacing by N samples is an incorrect processing choice (poor
processing). Group2 considerations allow strides of any integer value.
Dynamic signal analyzers provide selectable overlaps to deal with this
correctly.
....
From that
you can infer the 2D point spread function of the whole 2D image,
which in this case is a 2D Gaussian function.
The usefulness of this function is limited by group3 realities.


which is very convenient for it has no zero crossings in the
space or frequency domain) of the image in question,

...
If there is a real application, that
is a calculation that will be performed on real data, the window will
be finite and the response of the truncated Gaussian will have zero
crossings.
These are group2 concerns with your approach.
....
Convenient for deconvolution? If I'm not mistaken it's a bit
problematic to recover the value of x from the result of x * 0. As for
the finiteness of things, it's no problem as you can just consider
that anything out of bounds is equal to zero.
Group2 concerns bring in zeros. You need an approach that is robust to
the presence of zeros in the finite sampled domains.
....
By
"controlling the second moment of the window" to "select the scale of
details" you're making a choice between time resolution and frequency
resolution. What I'm trying to talk about is a way not to have to make
that choice and get all the detail, by catching it all at once and
sharpening it, if you will. I'm just trying to figure out what would
be the limitations of this.
People have been giving you examples from groups 2 and 3

I have no idea what you're referring to by
"process poorly".
See the 'chunks spaced by N' remarks and inability to deal with zeros
....
This part discussed at top of message:
I'm talking about theory here, not implementation. But I won't hold it
against you either, it seems like it's a custom around here to ponder
practicality and feasibility before establishing the theoretical
possibility of something.

Dale B. Dalrymple
.

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