Quantitative correlation test of colored noise using differentiation method

Although the algorithms for testing the correlation of colored noise have been widely used to test whether it is correlated, there are no quantitative researches for the differences between the practical correlation and the desired correlation. A new method for quantitative correlation test of colored noise is proposed in this paper - the differentiation method. The theoretical analysis shows that if the residual sequence is a white noise sequence, the desired correlation function is differed by the correlation function of the residual sequence from the practical correlation function, which is verified by the simulation result. So the quantitative correlation test of colored noise is implemented by testing whether the subtraction of the practical and the desired correlation functions is correlation function of a white noise sequence.