Abstract
The presence of radio noise affects the measurement of the air shower induced radio pulse at each antenna and predominantly determines the error of the measurement. Noise can interfere constructively or destructively with the radio pulse and increases or decreases the pulse amplitudes. On average noise increases the measured pulse amplitudes since the power of the noise adds to the pulse power. It will be shown that this effect depends on the signal-to-noise ratio, and that noise systematically flattens the lateral distribution of the radio signal. Therefore, an adequate treatment of noise is especially important for experiments in a noisy environment, like LOPES.
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Notes
- 1.
A summary of this chapter is published in Nuclear Instruments and Methods A 662 (2012) S238–S241 [7].
- 2.
For experiments aiming at the detection of molecular bremsstrahlung at GHz frequencies, measuring the integrated pulse power will not significantly change the signal-to-noise ratio and the detection threshold, since the pulse duration is expected to be much longer than the reciprocal of the observing frequency.
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- 4.
In addition, two other methods have been tested to determine \(A_\mathrm{true }(A_\mathrm{meas })\) and \(\Delta A_\mathrm{true }(A_\mathrm{meas })\), but failed: First, the inverse function of \(A_\mathrm{meas }(A_\mathrm{true })\), which would be available directly, is not defined for \(A_\mathrm{meas } < 1\). But this range is important for analysis, as \(12\,\%\) of the measurements in individual antennas have a signal-to-noise ratio \(A_\mathrm{meas } < 1\) (see Fig. 6.9). Second, using confidence intervals instead of mean and standard deviation failed. The problem is that for any confidence level \(\gamma \), there exists a minimum amplitude \(A_\mathrm{min }\), for which the probability that a pulse amplitude is reduced by noise to a value \(A_\mathrm{meas } < A_\mathrm{min }\) is smaller than \(1-\gamma \). Therefore, \(A_\mathrm{true }(A_\mathrm{meas })\) would be undefined for \(A_\mathrm{meas }\) close to \(0\), at least for centered confidence intervals. However, uncentered confidence intervals yield questionable results at high signal-to-noise ratios, since \(A_\mathrm{true }\) would systematically deviate from the mean \(A_\mathrm{meas }\).
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Schröder, F.G. (2012). Treatment of Noise. In: Instruments and Methods for the Radio Detection of High Energy Cosmic Rays. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33660-7_6
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DOI: https://doi.org/10.1007/978-3-642-33660-7_6
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