Notes of Biomedical signal processing

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INTRODUCTION Biological systems: complex because of interactions among them, dynamical behavior (adaptive to external and internal changes), high inter- and intra-individual variability (the latter causes the non- stationarity of biological processes), predictable in relative terms, signals corrupted by endogenous or exogenous noise (we assume an addictive model); flow chart of the decision process: Type of signals: ECG: determinist quasi-periodic, Action potential: deterministic transient, EEG: stochastic stationary (in short windows), EMG: stochastic non-stationary (in short windows) Methodology approaches: deterministic, when the parameters of interest are a priori known, it is only necessary to measure them; stochastic, when the parameters are not a priori known, it is necessary to use statistical methods; biological systems are mainly deterministic or mainly stochastic Strictly stationary process: all statistical moments are constant on the whole temporal window; weakly stationary process: mean and ACF are constant on the whole temporal window Ergodic process: all the statistical properties can be estimated using a single realization For a discrete-time signal mean and autocorrelation function (i.e., the correlation between two instants of the process depending on the delay that divides them) are defined as: In practice, mean and autocorrelation function are estimated from a finite number of samples; the sample mean estimates the real mean with uncertainty σ/√N, where σ = r(0) is the variance: Frequency bands and ranges of signals: ECG (frequency range: 0.05-200 Hz) up to 5 mV for adults and to 10 μV for fetuses, EEG (0.5-70 Hz) up to 100 μV, EMG (10-200 Hz) up to 5 mV but it’s highly dependent on the electrode placement, ABP (DC-20 Hz for indirect measures,…