Table A3.

Formulas: Spatio-Temporal and Frequency Features.

Abbreviation	Description	Formulas: Spatio-Temporal and Frequency
Spatio-Temporal Features
Range	Range (m/s2, rad/s) (Features: 10, 12, 14, 16, 18, 20, 56, 58, 60, 62, 64, 66, 96, 98, 100, 102, 104, 106)	$$maxx-minx$$
STD	Standard deviation (m/s2, rad/s) (Features: 2, 5, 9, 48, 51, 55, 94, 160, 162)	$$\sqrt{\frac{\Sigma {(x_t-\overline{x})}^2}{N-1}}$$
RMS	Root mean square (m/s2, rad/s) (Features: 11, 13, 15, 17, 19, 21, 57, 59, 63, 65, 67, 97, 99, 101, 103, 105, 107)	$$\sqrt{\frac{\Sigma x_t^2}{N}}$$
Velocity	Velocity per stride [41] (m/s) (Features: 8, 9, 54, 55)	$$\mathrm{v}\left(\mathrm{t}\right):\int \mathrm{a}\left(\mathrm{t}\right)\mathrm{dt}+\mathrm{C}1$$
Distance	Distance per stride (m) (Features: 4, 5, 50, 51)	$$\mathrm{x}\left(\mathrm{t}\right):\int \mathrm{v}\left(\mathrm{t}\right)\mathrm{dt}+\mathrm{C}2$$
KMPH	Kilometres per hour (km/h) (Features: 6, 52)	$$\left(\right(\Sigma \mathrm{Displacement}\ast 30)/1000)$$
Cadence	Number of steps per minute (Features: 7, 53)	$$\frac{\mathrm{number}\mathrm{of}\mathrm{steps}}{2}$$
Frequency features
FFT	Fast Fourier Transform of acceleration [39]	$${\Sigma }_{t=0}^{N-1}{a}_t{e}^{-i2\pi \ast \frac{tk}{N}}k=0,...,N-1$$
Dominant peak freq	Dominant frequency in the signal indicating step or stride frequency (Hz) (Features: 22, 68, 108)	$$max\left(\mathrm{FFT}\right)$$
Dominant peak width	Width of the peak of the dominant frequency (HZ) (Features: 23, 69, 109, 115, 121)	Distance between the left and right base of the dominant peak frequency.
Dominant peak slope	Slope the dominant frequency (HZ) (Features: 24, 70, 110, 116, 122)	Slope from the base to the top of the dominant frequency.
Dominant peak density	Density of the peak of the dominant frequency	Density from the base to the top of the dominant frequency
HR	Harmonic ratio: Measure to quantify smoothness of walking (Features: 112, 118, 124) [54]	Ratio of the sum of the amplitudes of the even harmonic to the sum of the amplitudes of the odd harmonics.
IH	Index of harmonicity: Measure to quantify symmetry of walking (Features: 113,119,125) [55]	Ratio of the aplitude of the dominant frequency to the sum of the first five superharmonics.

Abbreviations: x = Input; t = 1 observation; N = Total number of observations; a = Acceleration; AP = Anterior–posterior; ML = Medio-lateral; All code is available on Github: https://github.com/RichardFel/Reliability-of-Gait (accessed on 10 December 2021).