Abstract
A statistical analysis of a weighted averaging procedure for the estimation of small signals buried in noise (Hoke et al. 1984a) is given. The weighting factor used by this method is in inverse proportion to the variance estimated for the noise. It is shown that, compred to conventional averaging, weighted averaging can improve the signal-to-noise ratio to a high extent if the variance of the noise changes as a function of time. On the other hand, uncritical application of the method involves the danger that the signal amplitude is underestimated. How serious this effect is depends on the number of degrees of freedom available for the estimation of the weighting factor. The effect can be neglected, if this number is sufficiently increased by means of an appropriate preprocessing.
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References
Gevins AS (1984) Analysis of the electromagnetic signals of the human brain: Milestones, obstacles, and goals. IEEE Trans BME-31:833–850
Hoke M, Ross B, Wickesberg RE, Lütkenhöner B (1984a) Weighted averaging — theory and application to electric response audiometry. Electroenceph Clin Neurophysiol 57:484–489
Hoke M, Wickesberg RE, Lütkenhöner B (1984b) Time- and intensity-dependent low-pass filtering of auditory brain stem responses. Audiology 23:195–205
Knuth DE (1969) The art of computer programming. Addison-Wesley, Reading Menlo Park London Don Mills, Vol. 2
Nagelkerke NJD, de Weerd JPC, Strackee J (1983) Some criteria for the estimation of evoked potentials. Biol Cybern 48:27–33
Pantev Ch, Lütkenhöner B, Hoke M, Lehnertz K (1985) Comparison between simultaneously recorded auditory evoked magnetic fields and potentials elicited by ipsilateral, contralateral, and binaural tone-burst stimulation (submitted for publication to Audiology)
de Weerd JPC (1981) A posteriori time-varying filtering of averaged evoked potentials. Biol Cybern 41:211–222
Whalen AD (1971) Detection of signals in noise. Academic Press, New York San Francisco London
Woody CD (1967) Characterization of an adaptive filter for the analysis of variable latency neuroelectric signals. Med Biol Eng 5:539–553
Yu KB, McGillem CD (1983) Optimum filters for estimating evoked potential waveforms. IEEE Trans BME-30:730–737
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Lütkenhöner, B., Hoke, M. & Pantev, C. Possibilities and limitations of weighted averaging. Biol. Cybern. 52, 409–416 (1985). https://doi.org/10.1007/BF00449599
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DOI: https://doi.org/10.1007/BF00449599