A sampling technique for generating Gaussian noise having a uniform power spectral density from approximately 0.1 cps to 5 kc is described. In principle one could extend the uniform power spectral density property at both ends of the spectrum. The only nonlinear circuit required to implement the technique is a simple high level sampling circuit. Random noise is periodically sampled in order to generate a pulse train having short pulse durations and statistically independent pulse amplitudes. The random pulse train is then applied to a low pass filter in order to produce a Gaussianly distributed output as is predicted by the central limit theorem of probability. The technique is also useful for studying periodic overlapping impulse noise.