Reconstruction from zero crossings
Open-knowledge reference entry
The problem of reconstruction from zero crossings can be stated as: given the zero crossings of a continuous signal, is it possible to reconstruct the signal (to within a constant factor)? Worded differently, what are the conditions under which a signal can be reconstructed from its zero crossings?
This problem has two parts. Firstly, proving that there is a unique reconstruction of the signal from the zero crossings, and secondly, how to actually go about reconstructing the signal. Though there have been quite a few attempts, no conclusive solution has yet been found. Ben Logan from Bell Labs wrote an article in 1977 in the Bell System Technical Journal giving some criteria under which unique reconstruction is possible. Though this has been a major step towards the solution, many people are dissatisfied with the type of condition that results from his article.
According to Logan, a signal is uniquely reconstructible from its zero crossings if:
The signal x(t) and its Hilbert transform xt have no zeros in common with each other.
The frequency-domain representation of the signal is at most 1 octave long, in other words, it is bandpass-limited between some frequencies B and 2B.
Further reading
Logan, Jr, B.F. (April 1977). "Information in the Zero Crossings of Bandpass Signals" (PDF).
Begin with the source’s own compact description: “Reconstruction from zero crossings” is open-knowledge reference entry. The dossier treats that line as a proposition to test through Reconstruction, zero and crossings, not as a finished interpretation.
Why this record matters
The phrase “open-knowledge reference entry” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Aug 12, 2026. The linked authority identifier is Q7302791. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1977.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Reconstruction from zero crossings”, its source revision and the description used here.
- Expand the search: follow Reconstruction from zero crossings primary sources, Reconstruction from zero crossings archive and Reconstruction research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Reconstruction from zero crossings”?
- Which cited source is closest to the event, object or claim?
- What terminology or title could unlock a more precise catalogue search?
Search terms from this dossier
This entry incorporates text from “Reconstruction from zero crossings” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.