Simulation of 1/fα noise for analytical measurements

Abstract

A simple procedure is described that can be used to generate 1/fα noise, also known as power law noise, in simulated analytical measurement vectors. Certain types of power law noise, such as pink noise (α=1), dominate many types of analytical signals, so its simulation is important in optimizing data processing strategies. In this work, simulated 1/fα error sequences are created directly from white noise via the theoretical measurement error covariance matrix (ECM) by rotation and scaling. The 1/fα ECM is obtained from the coefficients of a finite impulse response filter and is easily adapted to generate multiplicative 1/fα noise that is probably more common for analytical systems exhibiting proportional noise characteristics. Simulating 1/fα noise directly from the ECM offers two main advantages. First, 1/fα noise can be easily simulated in the presence of other common analytical measurement errors by additive combination of the ECMs. Second, the theoretical ECM can be used to model real experimental measurement noise. It is shown that the power spectral density function of measurement error sequences generated by the proposed method closely approximates the theoretical behaviour of 1/fα noise. To demonstrate the utility of this method in evaluating data processing methods, simulated data exhibiting 1/f (pink) noise is analyzed by maximum likelihood principal component analysis (MLPCA) that takes measurement error structure into account, and baseline noise is simulated using brown noise to test baseline fitting by asymmetric least squares (AsLS).