Abstract
A modification of the edge detector of Chung & Kennedy is proposed in which the output provides confidence limits for the presence or absence of sharp edges (steps) in the input waveform. Their switching method with forward and backward averaging windows is retained, but the output approximates an ideal output function equal to the difference in these averages divided by the standard deviation of the noise. Steps are associated with peak output above a pre-set threshold. Formulae for the efficiency and reliability of this ideal detector are derived for input waveforms with Gaussian white noise and sharp edges, and serve as benchmarks for the switching edge detector. Efficiency is kept high if the threshold is a fixed fraction of the step size of interest relative to noise, and reliability is improved by increasing the window width W to reduce false output. For different steps sizes D, the window width for fixed efficiency and reliability scales as 1/D2. Versions with weighted averaging (flat, ramp, triangular) or median averaging but the same window width perform similarly. Binned above-threshold output is used to predict the locations and signs of detected steps, and simulations show that efficiency and reliability are close to ideal. Location times are accurate to order square root of W. Short pulses generate reduced output if the number of data points in the pulse is less than W. They are optimally detected by choosing W as above and collecting data at a rate such that the pulse contains approximately W data points. A Fortran program is supplied.
Full Text
The Full Text of this article is available as a PDF (333.9 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Chung S. H., Kennedy R. A. Forward-backward non-linear filtering technique for extracting small biological signals from noise. J Neurosci Methods. 1991 Nov;40(1):71–86. doi: 10.1016/0165-0270(91)90118-j. [DOI] [PubMed] [Google Scholar]
- Finer J. T., Simmons R. M., Spudich J. A. Single myosin molecule mechanics: piconewton forces and nanometre steps. Nature. 1994 Mar 10;368(6467):113–119. doi: 10.1038/368113a0. [DOI] [PubMed] [Google Scholar]
- Fredkin D. R., Rice J. A. Maximum likelihood estimation and identification directly from single-channel recordings. Proc Biol Sci. 1992 Aug 22;249(1325):125–132. doi: 10.1098/rspb.1992.0094. [DOI] [PubMed] [Google Scholar]
- Horn R., Lange K. Estimating kinetic constants from single channel data. Biophys J. 1983 Aug;43(2):207–223. doi: 10.1016/S0006-3495(83)84341-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Svoboda K., Schmidt C. F., Schnapp B. J., Block S. M. Direct observation of kinesin stepping by optical trapping interferometry. Nature. 1993 Oct 21;365(6448):721–727. doi: 10.1038/365721a0. [DOI] [PubMed] [Google Scholar]