Re: Cubic Spline Interpolation and Zero Crossing Analysis

On Jun 28, 7:03 am, fizteh89 <d...@xxxxxxxxxxxxxxxxx> wrote:
On Jun 28, 7:06 am, "David Lee"
....
<davidlee_malv...@xxxxxxxxxxxxxxxxxxxxxxxxxx> 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

.

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