Numerical Calculus and Simulation
Gérard Blanchet, Maurice Charbit · 2015
This chapter focuses on the problems of numerical calculus. Numerous functions like the conversion from a continuous-time system to a discrete time system, seeking of zeros, of minima and maxima, solving of ordinary differential equations (ODEs), interpolations, and solving of linear systems are provided in the basic version of matrix laboratory (MATLAB). Design methods based on continuous-discrete time changes actually consist of constructing a discrete-time simulator of a linear differential equation. This method provides satisfying results because the simulated systems are linear. In signal-processing, interpolation is generally performed by zero-insertion, followed by low-pass filtering. The most conventional techniques use polynomials: Lagrange basis polynomials, Newton's equations, cubic spline interpolation, etc.