Dear all, my name is Gabriel Delgado and one of the topics of study of my research group is the analysis of the acceleration peaks during the running. So far what we have done has been an analysis of the amplitude of the signal but I would like to do a deeper analysis and include the variable "Power spectral density (PSD)" as does the research group of the prestigious scientist Hamill.
I copy and paste what he does in two of his researches:
Mercer, J. A., Vance, J., Hreljac, A., & Hamill, J. (2002). Relationship between shock attenuation and stride length during running at different velocities. European Journal of Applied Physiology, 87(4–5), 403–408. https://doi.org/10.1007/s00421-002-0646-9
"Power spectral densities of ten repetitive patterns of leg and head accelerometer data were calculated via Fast Fourier Transformation for each subject–condition combination following procedures described by Shorten and Winslow (1992) and Derrick et al. (1998). Illustrated in Fig. 1 are horizontal bars representing example sections of data extracted from the accelerometer profiles used to calculate PSD. The mean and linear trends were removed from each sectionof data extracted from the accelerationprofiles and each data set was padded with zeros to result in a total of 1,024 data points. Power spectral densities were calculated for head (PSDhead) and leg (PSDleg) accelerometer profiles using a square window and adjusted to account for changes in power due to the zero-padding procedure. Finally, adjusted PSD were interpolated so each frequency bin was 1 Hz. These procedures follow the methods published elsewhere (Shorten and Winslow 1992; Derrick et al. 1998). Shock attenuation was quantified by calculating the ratio of PSDhead to PSDleg for each frequency within the 10–20 Hz frequency range. The ratios were then averaged across the frequencies to represent shock attenuation for that data set. A low ratio (i.e., closer to zero) betweenPSDhead and PSDleg indicates greater at- tenuation of the impact magnitude compared to a high ratio."
Busa, M. A., Lim, J., van Emmerik, R. E. A., & Hamill, J. (2016). Head and Tibial Acceleration as a Function of Stride Frequency and Visual Feedback during Running. Plos One, 11(6), e0157297. https://doi.org/10.1371/journal.pone.0157297
The power spectral density (PSD) of the head and tibial accelerations during stance was determined using a square window; frequency characteristics were normalized into 1 Hz bins [10]. Signal power magni- tude in both the active and impact phases ofstance were quantified by the integral ofthe signal power in the 3–8 Hz and 9–20 Hz frequency ranges, respectively. For both the tibia and head the impact peak was identified as the peak acceleration occurring in 0–30% ofstance and contained in the 9–20 Hz range in the PSD. The active acceleration peak was identified as the second peak in the head acceleration profile occurring between 31– 100% ofstance and in the 3–8 Hz range in the PSD [23]. Full procedures for processing the tib- ial and head accelerations are described in detail elsewhere [23]. The gain or attenuation of shock (i.e., the transmission of acceleration through the kinematic chain) from the tibia to the head was determined from a transfer function (Eq 1) which was used to calculate the PSD ratio ofeach frequency bin between the tibia and head signal [8, 10, 14, 28].
Transfer Function (dB) = 10 x log10 (PSDHead/PSDTibia)
I would like to do this in a very simple software I use (KST2). Below are the options that the software gives you to calculate the Power Spectral Density. Can anyone help me, what values should I include in the software? In my case I am recording with two accelerometers at a frequency of 400 Hz (less than Hamill, who records at about 1000 Hz).
Thanks in advance,
Gabriel Delgado
Here is more information about KST and the feature Power Spectral Density
https://kst-plot.kde.org/kst1/handbook/data-types.html
An interesting post about how to select the FFT length:
https://dsp.stackexchange.com/questions/3321/choosing-the-length-of-a-signal-when-calculating-the-fft
In this web they recommend Hanning and Blackmann options for vibrations testings:
https://vru.vibrationresearch.com/lesson/calculating-psd-time-history/
Here is a very interesting blog and free software related:
https://blog.endaq.com/vibration-analysis-fft-psd-and-spectrogram?hs_amp=true
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