A transformation which transforms from a two-dimensional continuous uniform distribution to a two-dimensional bivariate normal distribution (or complex normal distribution). If and are uniformly and independently distributed between 0 and 1, then and as defined below have a normal distribution with mean and variance .
(1)
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(2)
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This can be verified by solving for and ,
(3)
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(4)
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Taking the Jacobian yields
(5)
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(6)
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