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Details about the Audio Noise Generator

If you have tried the RANDOM.ORG Audio Noise Generator, you may be curious about the white noise that it generates. What are the characteristics of the noise you get and how is it different from the raw atmospheric noise used to generate it? Perhaps it seems a little excessive first to use atmospheric noise to generate random numbers and then use those numbers to generate white noise. Aren't we just going back and forth between noise and numbers without really doing a lot?

If you are used to working with audio, you will know that noise isn't just noise, but that there are different types. An important characteristic of noise is its spectral density, meaning how the power is distributed across the frequency spectrum. Noise is often described with a colour, such as white or pink, depending on its spectral density. Wikipedia contains a good explanation of why the names of colours are used in this fashion.

The figure below shows the frequency distribution for a sound file containing atmospheric noise. In fact, this file was recorded directly from one of the RANDOM.ORG radios using a sampling rate of 44.1 kHz, a sample size of 16 bits and using a single channel, i.e., as a mono signal. The graph was made using the free audio tool Audacity.

Frequency analysis of raw atmospheric noise
Frequency analysis of raw atmospheric noise
[play 1MB wav file]

As you can see, the spectral density is not particularly regular. Atmospheric noise can vary a good deal in its characteristics, and there is probably no accurate colour (at least not in general use) to describe this particular shape. We can observe a general decrease in power for higher frequencies, which is one of the characteristics of pink noise, but the sharp drop at 16 kHz and the small rise around 19 kHz are not typical for pink noise.

Because raw atmospheric noise cannot be expected to have a uniform spectral density, RANDOM.ORG performs processing on it. This is described in more detail on the Real-Time Statistics pages, in particular one that discusses the Source Purity test. The end product of this processing is a stream of uniformly distributed true random numbers, which are used for all the different services you find on RANDOM.ORG

The Audio Noise Generator works by using these random numbers as sound samples to construct a whole sound file. The distribution is uniform, meaning that for each invidiual sound sample, all the possible values (e.g., [0,255] for an 8-bit sample) have exactly the same chance of occurring. One result of this is that the whole sound file will have a uniform spectral density, i.e., approximately the same power level across all frequencies. The figure below shows a plot of the frequency distribution for a sound generated with the Audio Noise Generator on 12 June 2008, using the same audio parameters as were used to record the raw atmospheric noise mentioned above.

Frequency analysis of sound generated with RANDOM.ORG
Frequency analysis of sound generated with RANDOM.ORG
[play 1MB wav file]

As you can see, the power level is highly uniform across the range of frequencies. This type of noise is called white noise, because the uniform shape of the power level distribution is similar to that of white light. As we would expect, the RANDOM.ORG Audio Noise Generator produces perfect white noise. If you play the two sounds and compare, you will also be able to tell the difference. The pure white noise sounds a little sharper (and perhaps more unpleasant) because it contains more power at the high frequencies than the raw atmospheric noise.

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