spectral0

# spectral0 - The Spectral Test for Randomness Lign 17 A...

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The Spectral Test for Randomness Lign 17, A. Kehler Random values are the result of an arbitrary selection from among a set of alternatives. For our purposes, we’ll assume that the alternatives are the values 0 and 1, i.e., bits. A random sequence is simply a sequence of randomly-generated values. How can we tell if particular series of bits is likely to have been generated at random? First impressions can be misleading. Suppose that we are looking at a series of 10000 bits, and we see a series of 12 ones in a row: 111111111111. That many ones in a row might not look very random, but it turns out that the odds are less than 1 in 11 that we would not see a series of ones that long somewhere in the sequence. The question is whether this pattern – indeed, any pattern – shows up either much more or much less frequently than the laws of statistics would suggest. We would thus like a more mechanistic test that could indicate whether a sequence is randomly-generated, keeping in mind that the answer will necessarily be probabilistic , since there is always a chance that any given sequence of values was drawn randomly – it is just that the odds might be very small. One such method is the Spectral Test for randomness. The basic idea is that we can do frequency analysis with respect to various patterns, and

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spectral0 - The Spectral Test for Randomness Lign 17 A...

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