Spectral Arc Length (SPARC) movement smoothness

A duration- and amplitude-robust smoothness measure computed from the normalized Fourier magnitude spectrum of a speed profile. More negative = less smooth. A smooth minimum-jerk movement is approximately -1.4.

Usage

sparc(speed, fs, padlevel = 4, fc = 10, amp_th = 0.05)

Arguments

speed

Numeric speed (tangential velocity magnitude) profile.

fs

Sampling frequency in Hz.

padlevel

Zero-padding exponent added to the FFT length (default 4).

fc

Maximum cutoff frequency in Hz (default 10).

amp_th

Normalized amplitude threshold for the adaptive cutoff (0.05).

Value

The spectral arc length (negative scalar); NA if undefined.

References

Balasubramanian S, Melendez-Calderon A, Roby-Brami A, Burdet E (2015). "On the analysis of movement smoothness." J NeuroEng Rehabil 12:112.

Examples

t <- seq(0, 1, length.out = 200); tau <- t
speed <- 30 * tau^2 - 60 * tau^3 + 30 * tau^4  # minimum-jerk speed
sparc(speed, fs = 200)
#> [1] -1.403567