[time-nuts] Calculate spectral content from a series of zero crossing time stamps?

[Detlef.Amberg at gmx.de]

08.02.2011 08:17, Poul-Henning Kamp:
> In message <224676.41616.qm at web120905.mail.ne1.yahoo.com>, Tijd Dingen writes:
> 
>> >From what I could find so far, one method to go about this is use a
>> Lomb/Scargle Periodogram. And specifically the method by Press & Rybicki that
>> extirpolates the unevenly timed samples to an regular timed mesh, after which
>> a regular DFT is done.
> 
> Just knowing the time of the zero-crossings is very little information
> to go by, but you have to make some kind of assumption about the
> perfection of curve shape between those points, in order to say
> anything meaningful.

As far as I know a bandpass signal is described uniquely by its zero
crossings to within a constant. That is due to the Weierstrass
factorization theorem. A more practical foundation is outlined in
"B.F.Logan: 'Information in the zero crossings of bandpass signals', The
Bell System Technical Journal vol. 56 Number 4, April 1977" and some
other publications by the same author in the same journal.

Recently these techniques have been exploited in 'zepoc' algorithms for
low power hifi class D amplifiers and the 'click modulation' scheme.

But there were also publications which were in doubt that a real valued
signal can be reconstructed by its zero crossings.

Sadly, my mathematical background is not sufficient to follow the
arguments. But nonetheless zero crossing algorithms and nonuniform
sampling are very promising fields.

Cheers
Detlef