Simulating Gaussian stationary processes with unbounded spectra

This article proposes a new method for simulating a Gaussian process, whose spectrum diverges at one or multiple frequencies in [0, 1/2] (not necessar ily at zero). The method uses a generalization of the discrete wavelet tran sform, the discrete wavelet packet transform (DWPT), and requires only expl icit knowledge of the spectral density function of the process-not its auto covariance sequence. An orthonormal basis is selected such that the spectru m of the wavelet coefficients is as flat as possible across specific freque ncy intervals, thus producing approximately uncorrelated wavelet coefficien ts. This method is compared to a popular time-domain technique based on the Levinson-Durbin recursions. Simulations show that the DWPT-based method pe rforms comparably to the time-domain technique for a variety of sample size s and processes-at significantly reduced computational time. The degree of approximation and reduction in computer time may be adjusted through select ion of the orthonormal basis and wavelet filter.