Information Theoretical Sliding Window Optimization Applied to Discretization of Continuous Signals

Sliding window analysis is common to many time domain signal analysis methods. Determination of the optimal window width requires several different conditions to be met. Intuition into the signal or knowledge of limitations of computational resources could help; or an optimization scheme may be carried out. Balance between information loss and computational complexity must be met in any case. In a recent study, the authors proposed an optimal windowing method through minimization of the average mutual information between sliding windows. It was meant to determine the optimal input layer width of an artificial neural network to extrapolate time domain data from electromagnetic simulations. They extended it to an optimal sampling scheme. In the one step limit, discretization of continuous signals is another kind of windowing. A continuous signal sampled with infinite-frequency, -which is the signal itselfhas the maximum average mutual information between sliding windows. This can be interpreted as waste of resources. Decreasing the sampling rate generally results in a nonlinear decay of the average mutual information between windows. The first minimum, at which the decay settles down before increasing again, generally corresponds to the optimal sampling rate.