same variance , w is said to be a Gaussian white noise vector. In that case, the joint distribution of w is a multivariate normal distribution; the independence between the variables then implies that the distribution has spherical symmetry in n-dimensional space. Therefore, any orthogonal transformation of the vector will result in a Gaussian white random vector. In particular, under most types of discrete Fourier transform, such as FFT and Hartley, the transform W of w will be a Gaussian white noise vector, too; that is, the n Fourier coefficients of w will be independent Gaussian variables with zero mean and the same variance . The power spectrum P of a random vector w can be defined as the expected value of the squared modulus of each coefficient of its Fourier transform W, that is, Pi = E(|Wi|2). Under that definition, a Gaussian white noise vector will have a perfectly flat power spectrum, with Pi = σ2 for all i. If w is a white random vector, but not a Gaussian one, its Fourier coefficients Wi will not be completely independent of each other; although for large n and common probability distributions the dependencies are very subtle, and their pairwise correlations can be assumed to be zero. Often the weaker condition "statistically uncorrelated" is used in the definition of white noise, instead of "statistically independent". However, some of the commonly expected properties of white noise (such as flat power spectrum) may not hold for this weaker version. Under this assumption, the stricter version can be referred to explicitly as independent white noise vector. Other authors use strongly white and weakly white instead. An example of a random vector that is "Gaussian white noise" in the weak but not in the strong sense is where is a normal random variable with zero mean, and is equal to or to , with equal probability. These two variables are uncorrelated and individually normally distributed, but they are not jointly normally distributed and are not independent. If is rotated by 45 degrees, its two components will still be uncorrelated, but their distribution will no longer be normal. In some situations one may relax the definition by allowing each component of a white random vector to have non-zero expected value . In image processing especially, where samples are typically restricted to positive values, one often takes to be one half of the maximum sample value.