Discrete time techniques for time delay estimation
Abstract
Basic aspects of time delay estimation (TDE) based on sampled signals are investigated. The direct cross-correlation method is analyzed and compared to the average square difference function (ASDF) and the (addition only based) average magnitude difference function (AMDF) estimators, Their relative accuracy is theoretically evaluated, and previous empirical results are explained. It is shown that both the ASDF- and the AMDF-based estimators outperform the direct cross-correlation based estimator for medium-high signal-to-noise ratios. Moreover, the AMDF-based estimator, which avoids any multiplications, significantly reduces the computational complexity of the estimation procedure while offering only a moderate performance loss with respect to the ASDF based estimator.>
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The estimated cross-correlation function can be approximated by a concave parabola in the neighborhood of its maximum because its mathematical expectation is band limited and presents a symmetric peak around the true time delay.
“Since its mathematical expectation is shown to be band limited and present a symmetric peak around the true time delay, the estimated crosscorrelation function can be approximated by a concave parabola in the neighborhood of its maximum [40, 63, 64].”
From Time Delay Estimation in Room Acoustic Environments: An Overview (2006) · cites this paper as [40]
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- Authors
- Jacovitti, G., & Scarano, G.
- Affiliations
- Sapienza University of Rome (IT)
- ORCID
- Scarano, G.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 1993
- Volume
- 41
- Issue
- 2
- Pages
- 525-533
- ISSN
- 1053-587X (ISSN-L)
- OpenAlex
- W2148886336
- Cited by
- 433
- References
- 11
- Citations by year
- 2026: 6 · 2025: 15 · 2024: 5 · 2023: 17 · 2022: 8 · 2021: 15 · 2020: 17 · 2019: 21 · 2018: 22 · 2017: 20 · 2016: 21 · 2015: 29 · 2014: 30 · 2013: 23 · 2012: 14
- FWCI
- 5.20
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Signal Processing (publishedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Advanced Adaptive Filtering Techniques
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Signal Processing Techniques
- Physical Sciences › Computer Science › Signal Processing › Speech and Audio Processing
- Keywords
- time delay estimation, discrete-time signal processing, sampled signals, cross correlation function, average magnitude difference function, estimator accuracy, computational complexity, signal-to-noise ratio
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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