Approximates derivatives with finite differences of sampled values.
Finite differences approximate derivatives: forward (f(x+h)-f(x))/h, backward, and central (f(x+h)-f(x-h))/(2h) which is second-order accurate. Too small h magnifies round-off; noise in data amplifies in differentiation.
Estimating velocity from sampled position data.
Derivatives of sampled data are needed for velocity from position and for controller design, but numerical differentiation amplifies noise.
Approximates derivatives with finite differences of sampled values.
Derivatives of sampled data are needed for velocity from position and for controller design, but numerical differentiation amplifies noise.
Dividing small differences by a small step amplifies measurement noise, so smoothing or filtering is usually needed first.
It estimates the derivative from points on both sides of the target, which gives second-order accuracy instead of first-order.
Typical applications include estimating velocity from encoder positions sampled at fixed intervals, computing the slope of a measured temperature profile and estimating curvature for a tracing path in CNC machining.
Study "Interpolation" first (topic 92 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Second derivative (f₊-2f+f₋)/h². Balance truncation and round-off. Smooth data before differencing.
Estimating velocity from sampled position data.
The next topic is "Numerical integration", which builds directly on this one.
It is classed as Advanced in Engineering Mathematics (topic 93 of 104). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mathematics.
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