Notes of Biomedical signal processing

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SEGNALI Intro Signal: an ordered sequence of numbers that describes the variations and trends of a quantity. The order of numbers is determined by the order of measurements in time. Task of signal processing: to extract important knowledge that may not be clearly visible to the human eye Variability (inter-individual) is due to: - Non-stationarity of the process under analysis: the patient status and environmental influences can change - Complexity: capability to adapt in response to a great variety of stimuli and circumstances Disturbances: - Endogenous: if the origin is internal to the biological system - Exogenous: if the origin is external - White noise: its main characteristic is that its ACF is 1 in 0 and 0 elsewhere X(t) and v(t) are most often uncorrelated, but not always, such as ECG and respiration Statistical properties: - Probability distribution function: F(x)=P[X≤x] is the probability that the random variable X would minor or equal to x. if the stochastic variable is continuous 𝐹(𝑥) = ∫ 𝑓(𝑡)𝑑𝑡 - Probability density function: 𝑓(𝑥) = 𝑑𝐹(𝑥) 𝑑𝑥 - Autocorrelation function: Where f(u,v) is the density function of the joined probability of the two variables Xt1 and Xt2. If the signal is discrete in the formula we consider Xn1 and Xn2 instead. Characteristics of a signal: - Deterministic: the parameters of interest are a priori known, it is only necessary to measure them. It is possible to predict the future evolution on the basis of the previous events. - Stochastic: the parameters are not a priori known, it is necessary to use statistical methods. The prediction is not possible on the basis of the previous events. Stationarity of a stochastic signal: o In strict sense: if all the statistic moments are constant and not dependent on time in the whole temporal…