Relative signal levels of a sinusoid with and without background noise

In the process of looking at some order data, a question about the accuracy of the measurement of the signal level of discrete frequency signals which were close to the general noise level.  To answer this question, a small DATS worksheet was created which generated 2 signals.  The first signal was a 35 Hz sinusoid which, by itself the spectrum level was measured to be approximately -9 dB (ref 1 V) as seen in Figure 1.

Spectrum level of 35Hz sinusoid
Fig 1: Spectrum level of 35Hz sinusoid

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Does The Signal Have A Gaussian Probability Density?

The PROB module in DATS for Windows provides, amongst other options, a probability density analysis. Also, the signal generation suite has a module, GENPRB, which generates a classical gaussian probability density curve (and others). How then may these be used to compare the probability density of our measured signal with that of a true Gaussian one. The method is quite straight forward and is a matter of scaling.

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