Analysis of discrete implementation of generalized cross correlator
Open accessAbstract
A common discrete implementation of the cross correlator uses a parabolic fit to the peak when the delay is not an integral multiple of the sampling period. This correspondence analyzes and assesses the pitfalls of this approach. It is shown that this yields a biased estimate of the time delay, with both the bias and variance of the estimate dependent on the location of the delay between samples, SNR, signal and noise bandwidths, and the prefilter or window used in the generalized correlator.
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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 [63]
The Introduction (p. 610) describes fitting a parabola near the correlation peak, and the Theory section describes fitting one to three samples around the estimated maximum. The analysis also invokes symmetry, but the passages do not state that the expectation is band-limited or give band limitation and a symmetric peak around the true delay as the reason the parabolic fit works. The paper cautions that this fit yields a biased delay estimate. (LLM, conf=0.84)
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- Authors
- Boucher, R., & Hassab, J.
- ORCID
- Boucher, R.
- Venue
- IEEE Transactions on Acoustics, Speech, and Signal Processing
- Published
- 1981-06
- Volume
- 29
- Issue
- 3
- Pages
- 609-611
- ISSN
- 0096-3518 (ISSN-L)
- OpenAlex
- W2169054076
- Cited by
- 111
- References
- 3
- Citations by year
- 2024: 4 · 2023: 1 · 2022: 1 · 2021: 4 · 2020: 4 · 2019: 3 · 2018: 3 · 2017: 4 · 2016: 3 · 2015: 2 · 2014: 6 · 2013: 9 · 2012: 1
- FWCI
- 4.99
- Type
- journal article
- Language
- en
- Open access
- green
- zenodo.org
- Licence
- Locations
- IEEE Transactions on Acoustics Speech and Signal Processing (publishedVersion)
- Zenodo (CERN European Organization for Nuclear Research) (submittedVersion, public-domain)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Speech and Audio Processing
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Engineering › Computational Mechanics › Advanced Adaptive Filtering Techniques
- Keywords
- time delay estimation, signal-to-noise ratio, pre-filtering, windowing
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