Differentiate a numeric vector or matrix — differentiate • PhysioMoCap

Low-level function to compute numerical derivatives of arbitrary order using finite difference methods.

Usage

differentiate(x, dt, method = c("central", "forward", "backward"), order = 1L)

Arguments

x: Numeric vector or matrix (time x channels).
dt: Time step between samples (1 / sampling_rate).
method: Difference method: "central", "forward", or "backward".
order: Derivative order: 1 (velocity), 2 (acceleration), or 3 (jerk).

Value

Differentiated data with same dimensions as input. Boundary values where the stencil cannot be applied are set to NA.

Details

For method = "central" with order = 1: $$f'(i) = (x[i+1] - x[i-1]) / (2 \cdot dt)$$

For method = "central" with order = 2: $$f''(i) = (x[i+1] - 2 x[i] + x[i-1]) / dt^2$$

For higher orders, the derivative is computed by repeated application of the first-order formula.

References

Winter DA (2009). "Biomechanics and Motor Control of Human Movement." 4th ed. John Wiley & Sons.

See also

computeVelocity() for computing velocity from PhysioExperiment, computeAcceleration() for second-order derivatives, savgolFilter() for smoothed differentiation via Savitzky-Golay.

Examples

# Differentiate sin to get cos
t <- seq(0, 2 * pi, length.out = 200)
x <- sin(t)
dx <- differentiate(x, dt = t[2] - t[1], method = "central", order = 1)
# dx should approximate cos(t)