Accumulation of distortion in signal processing systems

The mean-square errors (MSE) of individual subsystems of a signal processing system generally don´t add up to equal the overall MSE, due to mutual correlations among the errors on the individual subsystems. This makes it difficult to interpret the magnitude of contribution of each subsystem to the MSE. It is shown that if the MSE of each subsystem is defined alternatively as the MSE between conditional mean estimators of the original signal at the input and output of that subsystem, then the overall MSE is in fact the sum of the MSE´s of individual subsystems. Several examples illustrate the usefulness of this principle in understanding the source of system impairments.