Positive functions in both their time and frequency representations? (i.e. Gaussian function)

On Nov 14, 6:36&#4294967295;pm, dbd <d...@ieee.org> wrote:
> In your process you apply a rectangular window in the time domain
> simply by selecting a finite data set of samples to transform. "No
> window" -is- a rectangular window.

Oh, sure, that's one way to see it hehe. Not like that kind of
windowing matters much here ;-).

On Nov 14, 5:04&#4294967295;pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> It seems you are re-inventing the Gabor filters. Or wavelets.
>
> Rune

I was rather under the impression that I was reinventing the original
1930s analog spectrograph, which if I'm not mistaken was also based on
(analog) band-pass filtering and envelope detection (or something to
that effect). I really wonder why I've never seen any such thing
implemented in a digital spectrograph before, I mean it's pretty
intuitive, intuitive enough so that I could come up with it when I
didn't understand what an FFT was yet.

On 14 Nov, 21:06, Michel Rouzic <Michel0...@yahoo.fr> wrote:
> On Nov 14, 5:04&#4294967295;pm, Rune Allnor <all...@tele.ntnu.no> wrote:
>
> > It seems you are re-inventing the Gabor filters. Or wavelets.
>
> > Rune
>
> I was rather under the impression that I was reinventing the original
> 1930s analog spectrograph, which if I'm not mistaken was also based on
> (analog) band-pass filtering and envelope detection (or something to
> that effect).

Maybe. I dabbled with Gabor filters some time in the mid '90s.
Don't remember the exact dates, but the Gabor reference was old;
I'd say from the '50s although he might have done is thing a lot
earlier than that.

> I really wonder why I've never seen any such thing
> implemented in a digital spectrograph before, I mean it's pretty
> intuitive, intuitive enough so that I could come up with it when I
> didn't understand what an FFT was yet.

You might have seen it, but under a different name. As you say,
it's intuitive, straight-forward, and it works. Lots of people
have come up with that same scheme independently, and there is
no reason to expect anyone to publish it (the technique is so
obvious it might not get through first screening if you tried).
So there is no reason to expect that there has been established
an 'accepted' term for the technique.

And as long as the filters are calibrated there is no need to
stick with Gauss filters. Lots of variations.

Rune

On Nov 14, 9:44&#4294967295;pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> You might have seen it, but under a different name. As you say,
> it's intuitive, straight-forward, and it works. Lots of people
> have come up with that same scheme independently, and there is
> no reason to expect anyone to publish it (the technique is so
> obvious it might not get through first screening if you tried).
> So there is no reason to expect that there has been established
> an 'accepted' term for the technique.
>
> And as long as the filters are calibrated there is no need to
> stick with Gauss filters. Lots of variations.
>
> Rune

The reason why I assumed that I've never seen it before is that
everytime I see a linear frequency scale spectrograph it seems to be
based on STFT (for obvious reasons), and everytime I saw a logarithmic
frequency scale spectrograph it seemed to be a linear spectrograph
that stretches things around. By the way, are you saying that it's so
obvious it explains the lack of a term or documentation for it? Allow
me to be sceptical, I mean, in DSP, it's like the more obvious and
simple something is the more it is documented, hehe.

What do you mean by "calibrated" filters?

On 15 Nov, 00:32, Michel Rouzic <Michel0...@yahoo.fr> wrote:
> On Nov 14, 9:44&#4294967295;pm, Rune Allnor <all...@tele.ntnu.no> wrote:
>
> > You might have seen it, but under a different name. As you say,
> > it's intuitive, straight-forward, and it works. Lots of people
> > have come up with that same scheme independently, and there is
> > no reason to expect anyone to publish it (the technique is so
> > obvious it might not get through first screening if you tried).
> > So there is no reason to expect that there has been established
> > an 'accepted' term for the technique.
>
> > And as long as the filters are calibrated there is no need to
> > stick with Gauss filters. Lots of variations.
>
> > Rune
>
> The reason why I assumed that I've never seen it before is that
> everytime I see a linear frequency scale spectrograph it seems to be
> based on STFT (for obvious reasons), and everytime I saw a logarithmic
> frequency scale spectrograph it seemed to be a linear spectrograph
> that stretches things around.

Seems to be a very popular way of doing things. At times one
wonders if DSP practitioners know of anything else than the FFT...

> By the way, are you saying that it's so
> obvious it explains the lack of a term or documentation for it? Allow
> me to be sceptical, I mean, in DSP, it's like the more obvious and
> simple something is the more it is documented, hehe.

I wouldn't disagree with that. Academia these days requires
publications. DSP is a practical discipline located in the
intersection between lots of others, so people re-invent
the same stuff over and over again.

On the other hand, if Gabor really did his filter trick
before WWII (did you know he was a Nobel laureate? 197x.
For inventing holography.) it was the time before everybody
started to publish every trivial detail, just for the
paper trail.

> What do you mean by "calibrated" filters?

I've seen filter banks be used in applications where
the time-frequency distribution of certain signals
were measured. Acoustic propagation loss measurements.
In such applications one used 1/M octave band filters,
which need to be scaled for amplitude and bandwidth
so as not to distort the energy measurements.

It's basically the same thing you try to do, but
implemented as a set of filters. Which means one
no longer enjoys the benefits the orthogonality
of the DFT offers. Which means one needs to
explicitly make sure that Parseval's equation
holds.

And no. I can't provide references to those
applications.

Rune

On Nov 14, 10:52 am, Michel Rouzic <Michel0...@yahoo.fr> wrote:
> On Nov 14, 6:36 pm, dbd <d...@ieee.org> wrote:
>
> > In your process you apply a rectangular window in the time domain
> > simply by selecting a finite data set of samples to transform. "No
> > window" -is- a rectangular window.
>
> Oh, sure, that's one way to see it hehe. Not like that kind of
> windowing matters much here ;-).

Michel

So, is your STFT like your windowing: that is what you use if we want
to look at it that way not that it matters much here? How else do you
get frequency domain samples?

The efficient, multiple output per octave approaches have been DFT
based, such as Browns implementation of Constant Q filters. These are
log spaced.

Dale B. Dalrymple

Rune Allnor wrote:
> Seems to be a very popular way of doing things. At times one
> wonders if DSP practitioners know of anything else than the FFT...

Hehe, good observation.

> > By the way, are you saying that it's so
> > obvious it explains the lack of a term or documentation for it? Allow
> > me to be sceptical, I mean, in DSP, it's like the more obvious and
> > simple something is the more it is documented, hehe.
>
> I wouldn't disagree with that. Academia these days requires
> publications. DSP is a practical discipline located in the
> intersection between lots of others, so people re-invent
> the same stuff over and over again.

Oh yeah, you're talking about peer-reviewed publications. I don't care
about these, I started off with the mentality that will prevail in our
new era, i.e., peer-reviewed publications are some expensive stuff I'm
only allowed to read the abstracts of, what matters as a
"documentation" is what Google returns that I can actually use. And on
these things, everything is thoroughly documented, down to the most
trivial operations. In this context, not having ever encountered
anything like the approach I chose, however obvious and expectably
ubiquitous, makes me somewhat doubt about its actual popularity. I
just figured that people rarely need anything different than STFT-
based spectrograms..

> > What do you mean by "calibrated" filters?
>
> I've seen filter banks be used in applications where
> the time-frequency distribution of certain signals
> were measured. Acoustic propagation loss measurements.
> In such applications one used 1/M octave band filters,
> which need to be scaled for amplitude and bandwidth
> so as not to distort the energy measurements.

I'm not entirely sure I entirely understood that, but regarding my
application I just consider that the "point-spread functions" (if we
can call it that) in my spectrograms are my frequency-domain windowing
function horizontally multiplied (if that makes any sense, I'm talking
about picturing the thing using the same representation as a
spectrogram) by the FFT of that windowing function, in the time
domain.

If you consider that, it's easy to see what I find desirable about
Gaussian windowing : the "point-spread function" of a spectrogram is a
smooth 2D Gaussian function, whereas anything else (that I know of)
has ripples, either horizontally or vertically. If you look at the
whole problem as having to filter an image with a point-spread
function (or at this point should I say impulse response?) which
horizontal aspect (as seen from the side, in 1D) has to be the FFT of
its vertical aspect, what would be the most aesthetically desirable
choice, besides a Gaussian function? That's the whole dilemma of
choosing a windowing function for time-frequency analysis as I
conceptualise it, and I believe it's a valid way to think of it.

On Nov 15, 12:19&#4294967295;am, dbd <d...@ieee.org> wrote:
> On Nov 14, 10:52 am, Michel Rouzic <Michel0...@yahoo.fr> wrote:
>
> > On Nov 14, 6:36 pm, dbd <d...@ieee.org> wrote:
>
> > > In your process you apply a rectangular window in the time domain
> > > simply by selecting a finite data set of samples to transform. "No
> > > window" -is- a rectangular window.
>
> > Oh, sure, that's one way to see it hehe. Not like that kind of
> > windowing matters much here ;-).
>
> Michel
>
> So, is your STFT like your windowing: that is what you use if we want
> to look at it that way not that it matters much here? How else do you
> get frequency domain samples?
>
> The efficient, multiple output per octave approaches have been DFT
> based, such as Browns implementation of Constant Q filters. These are
> log spaced.
>
> Dale B. Dalrymple

Sorry I'm afraid I misunderstood your earlier windowing comment then.
I'm not sure how to answer your question. here's what I do : I filter
my signal through a bunch of bandpass filters. For each of these
bands, I produce the analytic signal, then the magnitude of it, and
that's it, that's my spectrogram right there : each of its horizontal
bands is the time-domain envelope of a bandpass-filtered version of
the original signal. So there's only windowing in the frequency
domain, none in the time domain.

You only window in one domain, in the case of the STFT it's in the
time domain, in my case it's in the frequency domain (frequency domain
windowing  = bank of bandpass filters)

On Nov 14, 5:11 pm, Michel Rouzic <Michel0...@yahoo.fr> wrote:

> ...
> You only window in one domain, in the case of the STFT it's in the
> time domain, in my case it's in the frequency domain (frequency domain
> windowing  = bank of bandpass filters)

Michel

The windowing literature back to the 1950's contains frequency domain
windowing. The von Hann window, the Hamming window and the Blackman
family of windows were all designed to be performed by convolving
small kernels in the frequency domain. The Blackman-Harris windows
were designed by optimizing the frequency domain coefficients. In the
time domain a DFT must have at least rectangular windowing, but if it
does, it them makes the DFT a set of efficiently calculated bandpass
filters that can also be further windowed again in the frequency
domain by the above listed windows. One common name for the frequency
domain coefficient filters is the "cosine sum" windows. When non-
linearly sized and nonuniformly spaced filter outputs are desired, the
coefficients are altered for each desired output. The logrithmically
spaced constant-Q filters are efficiently calculated in this way. The
STFT has long been used as a set of bandpass filters to be frequency
domain weighted/shaped. The reason you misunderstood my earlier
remarks seems to be that you don't understand the nature, history and
applications of the STFT. That may also be why people have not
understood your statements about the STFT.

Dale B. Dalrymple