Bussgang test: A powerful non-gaussianity test

A process is said Bussgang if the cross-correlation function with its version passed through a zero-memory nonlinearity is proportional to the auto-correlation function of the process (invariance property). Gaussian processes are Bussgang processes too. As a consequence, Bussgangness tests may act as non-Gaussianity tests. Performance analysis shows that Bussgangness tests are more powerful than conventional Gaussian tests for correlated samples for a wide range of correlation coefficients and data lengths.