The white, ergodic, and jointly Gaussian signals generated by a simple chaotic system

A piecewise chaotic map, which has uniform invariant measure, can be used to generate a white noise and, by Perron-Frobenius equation, the invariant measure can be transformed to any kind of invariant measure by homeomorphism. Therefore, a Gaussian-like white noise can be implemented easily by famous chaotic piecewise maps as a white noise random number generator in computer. Moreover, given a correlation coefficient, white, ergodic and jointly Gaussian signals can be generated by computer. An approach to create these signals is also presented.