Cubic Spline Interpolation and Zero Crossing Analysis

On Jun 28, 7:06 am, "David Lee"
<davidlee_malv...@dontusethisbit.hotmail.com> wrote:
> Ron N wrote...
> > David Lee:
> >> Sampling rate is usually 44.1kHz and the frequency of the bat echolocation
> >> vocalizations can be as high as 110kHz.
>
> >> That's the original frequency of course - I'm not trying to beat Nyquist!  I'm
> >> dealing with the frequency divided signal (sampled at 44.1kHz)  which can
> >> contain frequencies as high as 11kHz.
> > What's the maximum rate-of-change of the frequency
> > which you're trying to track?
>
> A Natterer's bat, for example, uses an extremely linear broadband frequency sweep and can sweep from
> above 110kHz to below 20kHz  (ie 11 to 2 kHz after division) in times around 2.5 to 4ms. Insect
> "vocalizations" can exhibit much higher sweep rates - and maximum rate of change of frequency is one
> of the criteria used in the automatic recognition of bat calls to eliminate insect sounds.
>
> The purpose of the time/frequency representation of calls is identification of species and so the
> requirement is to be able to identify characteristic features of the calls and not to extract
> accurate detailed parameters - for which purpose we normally use FFT-based tools to analyse the
> original call (usually captured as a 10x time-expanded signal so as to be audible and easily handled
> as an audio sound file).
>
> Another major issue is that the recordings can be up to several hours in length, so a rapid analysis
> technique is required to extract frequency data and filter out the bat-call candidates from the
> background noise.
>
> There is a commercial bat detector system - the Anabat - that  carries out the analysis in real-time
> and can be left unattended in the field for months at a time (provided that it isn't blown up by the
> bomb disposal squad as happened recently here in the UK when the ecologists concerned failed to
> properly label their equipment!)  What I am trying to do is to extract zero-crossing data from a
> much cheaper, more accessible, detector into a form that can be used with the same freely available
> software as is used for the commercial device.
>
> Using linear interpolation to determine zero-crossing times, I am already obtaining acceptable
> results. I was just looking for a staightforward and rapid way of refining the interpolation and
> thought that a cubic spline may fit the bill.
>
> Thanks for your interest
>
> David

Try Poincare sections on a reconstructed attractor in multi-
dimensional state space...
It's a multi-dimensional generalization of a one-dimensional level-
crossing technique (zero-crossing in your case)

Ah, heck, this is just comp.dsp, I almost forgot it :-)

fizteh89 wrote...

> Try Poincare sections on a reconstructed attractor in multi-
> dimensional state space...
> It's a multi-dimensional generalization of a one-dimensional level-
> crossing technique (zero-crossing in your case)
>
> Ah, heck, this is just comp.dsp, I almost forgot it :-)

I'm sure that there must be a point that you are trying to make but I haven't a clue what it might 
be.

On Jun 28, 7:03 am, fizteh89 <d...@soundmathtech.com> wrote:
> On Jun 28, 7:06 am, "David Lee"
...
> <davidlee_malv...@dontusethisbit.hotmail.com> wrote:
> > Ron N wrote...
> > > David Lee:
> > >> Sampling rate is usually 44.1kHz and the frequency of the bat echolocation
> > >> vocalizations can be as high as 110kHz.
>
> > >> That's the original frequency of course - I'm not trying to beat Nyquist!  I'm
> > >> dealing with the frequency divided signal (sampled at 44.1kHz)  which can
> > >> contain frequencies as high as 11kHz.
> > > What's the maximum rate-of-change of the frequency
> > > which you're trying to track?
>
> > A Natterer's bat, for example, uses an extremely linear broadband frequency sweep and can sweep from
> > above 110kHz to below 20kHz  (ie 11 to 2 kHz after division) in times around 2.5 to 4ms.

So you're trying to estimate frequency as it changes from
under 2 cycles per millisecond to over 6 cycles per
millisecond in the first 1 millisecond (about 44 samples)?

Given that rate of change of frequency, I'll take back
my phase vocoder recommendation, as that techniques usually
requires a more stable frequency between the two fft windows.

I might try using some sort of software PLL to track your
sweep.  But I'm not even sure that a 44.1 kHz sampling
rate is high enough given those rates of frequency modulation.

> Insect
> > "vocalizations" can exhibit much higher sweep rates - and maximum rate of change of frequency is one
> > of the criteria used in the automatic recognition of bat calls to eliminate insect sounds.
>
> > The purpose of the time/frequency representation of calls is identification of species and so the
> > requirement is to be able to identify characteristic features of the calls and not to extract
> > accurate detailed parameters - for which purpose we normally use FFT-based tools to analyse the
> > original call (usually captured as a 10x time-expanded signal so as to be audible and easily handled
> > as an audio sound file).
>
> > Another major issue is that the recordings can be up to several hours in length, so a rapid analysis
> > technique is required to extract frequency data and filter out the bat-call candidates from the
> > background noise.
>
> > There is a commercial bat detector system - the Anabat - that  carries out the analysis in real-time
> > and can be left unattended in the field for months at a time (provided that it isn't blown up by the
> > bomb disposal squad as happened recently here in the UK when the ecologists concerned failed to
> > properly label their equipment!)  What I am trying to do is to extract zero-crossing data from a
> > much cheaper, more accessible, detector into a form that can be used with the same freely available
> > software as is used for the commercial device.
>
> > Using linear interpolation to determine zero-crossing times, I am already obtaining acceptable
> > results. I was just looking for a staightforward and rapid way of refining the interpolation and
> > thought that a cubic spline may fit the bill.
>
> > Thanks for your interest
>
> > David
>
> Try Poincare sections on a reconstructed attractor in multi-
> dimensional state space...
> It's a multi-dimensional generalization of a one-dimensional level-
> crossing technique (zero-crossing in your case)
>
> Ah, heck, this is just comp.dsp, I almost forgot it :-)

So how does the time/memory/Watts/MACs/LUTs/etc. per result
of using Poincare sections compare to measuring interpolated
zero crossings in terms of cost per result?


--
 rhn A.T nicholson d.0.t C-o-M