Just as an appropriate representation of a deterministic function can facilitate an application, such as with trigonometric Fourier series, decomposition of a random function can make it more manageable. Specifically, given a random function X(t), where the variable t can either be vector or scalar, we desire a representation of the form in Eq. (2.1), where x₁(t), x₂(t),... are deterministic functions, Z₁,Z₂, ... are uncorrelated zero-mean random variables, the sum may be finite or infinite, and some convergence criterion is given. Equation 2.1 is said to provide a canonical expansion (representation) for X(t). The terms Z_k, x_k(t), and Z_kx_k(t) are called coefficients, coordinate functions, and elementary functions, respectively. {Z_k} is a discrete white-noise process such that the sum is an expansion of the centered process X(t) minus[1] μ_X(t) in terms of white noise. Consequently, it is called a discrete white-noise representation.