Linear digital filtering for laboratory automation

The design of nonrecursive and recursive digital filters using linear least squares or linear minimum variance is described. This method of design requires a model, and since polynomial approximations are widely used in laboratory automation, a polynomial state model is first utilized. Then an exact scalar signal model is employed that results in a completely time-varying filter. For both models, the design leads to the recursive Kalman filter. The operation of the filters for noise reduction is first demonstrated for simulated data, and design forms are compared. For the exact scalar signal model, noise reduction and peak separation are demonstrated using simulated data and data obtained from a mass spectrometer. By using the correct model, excellent peak separation and noise reduction can be obtained.