Skip to contents

Harmonic ratio of a trunk-acceleration signal

Source: R/stability-nonlinear.R
harmonicRatio.Rd

The harmonic ratio quantifies the smoothness/rhythmicity of trunk acceleration over a stride from its Fourier series: because there are two steps per stride, the even harmonics carry the step-to-step-symmetric (in-phase) content and the odd harmonics the asymmetric content. For anterior-posterior and vertical acceleration the ratio is even/odd (higher = smoother); for medio-lateral it is odd/even (Menz et al. 2003; Bellanca et al. 2013).

Usage

harmonicRatio(
  signal,
  n_strides = 1L,
  direction = c("AP", "vertical", "ML"),
  n_harmonics = 20L
)

Arguments

signal

Numeric acceleration over an integer number of strides (a single stride if n_strides = 1).

n_strides

Number of strides spanned by signal (default 1); the Fourier fundamental is the stride frequency.

direction

"AP"/"vertical" (even/odd) or "ML" (odd/even).

n_harmonics

Number of harmonics summed (default 20).

Value

A harmonic_ratio object with ratio, even_sum, odd_sum and direction.

References

Menz HB, et al. (2003); Bellanca JL, et al. (2013).

See also

maxLyapunovExponent()

Examples

t <- seq(0, 1, length.out = 200)[-200]
# a clean 2-steps-per-stride (even-harmonic) signal
harmonicRatio(cos(2 * 2 * pi * t), direction = "AP")
#> <harmonic_ratio> (AP) ratio = 672942401973048.500 (even=99.5, odd=1.48e-13)