An introduction to model based digital signal processing

Initial digital signal processing (DSP) work was aimed at separating deterministic signals from noise and comprised filter design and fast Fourier transform (FFT) based spectral analysis. More recently DSP applications have expanded to include the filtering of random signals in noise. This challenging area of research has united many diverse fields such as astronomy and medicine and has "blurred" the boundaries between signal processing, time series analysis, optimisation theory and topology (in the study of the underlying dynamics of chaotic processes). The focus here is the application of DSP to random (stochastic) signals and complex deterministic (chaotic) signals found in biomedical applications. Optimum processors for filtering these signals assume specific models for the signal and noise sources. If these models are correct then one can achieve guaranteed levels of performance with quantified estimation error statistics. Incorrect models can give misleading results. This is a brief overview of model based DSP illustrated with a heart rate estimation example.