Auditory experiments often use broadband noise for various listening tests, and it is typically specified to have a Gaussian amplitude distribution. But can your ears tell the difference between that and a uniform White noise of the equivalent loudness? Both types of noise have the same flat frequency spectrum (they are both "white"), but the Gaussian has a much lower average amplitude for the same total dynamic range. In other words, its waveform reaches the same instantaneous peak amplitudes, but much less often.

This can make a big difference when trying to generate very loud noise, since if the system levels are set to prevent overdriving the amplifier or speakers on the peaks, the Gaussian noise will end up several dB softer. (Typically about 8 dB for the Daqarta Generator, with the Standard Deviation set to unity.)

A Gaussian noise can be created by adding multiple independent uniform sources together, so if each of those independent sources sounds the same, why should their sum sound anything other than louder?

The GausWhit.GEN setup allows you to compare two different noise sources to see if they sound qualitatively the same. It employs the general idea used in AltSine.GEN for comparing the amplitudes of two identical sine waves. Here the Left output consists of the sum of the two sources, smoothly alternating back and forth in a carefully overlapped fashion such that if they are equivalent, it will sound like one continuous source.

The two sources are separate Generator streams, each modulated by its own Burst generator. The bursts are staggered such that while one stream is falling, the other is rising. (There are no steady portions of the bursts, but that is not critical here.)

The burst parameters are set the same as in AltSine, with one critical difference: Instead of Cos^1.0, Burst Shape here uses Cos^0.5 (square root). This is because the two sources are uncorrelated, so they add in RMS fashion. Consider that when adding two identical sine waves, the result is twice the amplitude or 6 dB louder than either alone. But when adding two uncorrelated signals, only the maximum possible amplitude doubles, not the average. The result is only a 3 dB increase in loudness.

So, where the falling burst of one stream crosses the rising burst of the other, each must be only 3 dB (70.71% or the square root of 2) below the normal full-on level, rather than 50% as in AltSine. And at every other point where they overlap, the sum of the squares must be unity. The Cos^0.5 shape turns out to be exactly what is needed here.

Since the instantaneous peaks of the two streams can add to more than unity (2 * 70.71% = 141.42%), each Level control has been reduced to prevent clipping. The maximum permissible Level is the value which when multiplied by the 70.71% rise/fall midpoint gives 50%, and that value is again 70.71%. However, it is here set to a conservative 50% (-6 dB instead of -3 dB).

But the uniform White noise on Stream 0 has a higher average level than the Gauss noise on Stream 1, so the Stream 0 Level is reduced still further until the output sounds continuous. The proper value is about -14 dB, or 8 dB below the Gauss setting of -6 dB.

That value is for a Gauss noise with a Standard Deviation of unity; higher deviations require less reduction, and smaller deviations require more. With a deviation of 2.00 the best match was obtained with a Stream 0 Level of -8 dB, which is 6 dB above the unity deviation value of -14 dB, or a factor of 2 louder. With a deviation of 0.50 it was -20 dB, which is 6 dB below or a factor of 2 softer than with unity deviation.

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