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The New APAS Filtering Algorithm

It is well known that there is no optimal solution in filtering, therefore Ariel dynamics have developed in collaboration with Dr Giannis Giakas a Graphics User Interface (GUI) program that calculates an optimal cut-off frequency, but all the parameters are open to the experimenters to make some adjustments depending on their data. For us, it is important that the user learns with the program how to optimally filter, however, the program also provides some "templates of movements" in case the user does not want to learn anything about it and wants to use it as a black box. Obviously one of the many templates provided represents an example of the way that the parameters are used in other programs.

This technique is open to the experimenter to make some adjustments to his/her measurements. Some of the important parameters that the experimenter can control are:

- Type of digital filter (to choose between 3)

- Order of digital filter (2, 4, 6, 8)

- Different cut-off of higher derivatives

- Type of extrapolation (linear, mirror, inverse mirror, polynomial, linear prediction)

- Number of points extrapolated (from 0 up to number of data)

- Signal to noise ratio (if the quality of data is known then this will produce better filtering)

- Under-sampling (in case data have been collected with very high sampling frequency)

This GUI program comes as a plug in to APAS and is the only filtering program that can really be used for teaching as well. For example to show how the various parameters described above affect filtering. Off course there is also the option of entering the cut-off frequency manually. In the research of various movements, some adjustment of the parameters will give the best filtering results. If the research is focused to one movement, the parameters remain the same after an initial adjustment so a massive number of data and data files that describe the same process can be "optimally" filtered (e.g. laboratories involved only in gait analysis).

The user has the option to graphically display the results, which is recommended at the initial stages, viewing also the power spectrum of the signal as well as indicative comments and lines to understand how noise is modeled and where the cut-off is. After the template of movement is established the graphics option can be turned off.

Future developments include a time-frequency based approach, which will be an optimal solution for non-stationary signal such as impacts, throwing etc. In fact all signals are non-stationary anyway!

Some indicative references

Giakas G, Stergioulas L and A Vourdas (2000). Time-frequency filtering of non-stationary kinematic signals using the Wigner function: accurate assessment of the second derivative. Journal of Biomechanics 33(5), 567-574.

Giakas G (1999, invited speaker). Automatic data filtering in Sports Biomechanics: Filtering Solutions. Data Filtering Workshop. XVII International Symposium of Biomechanics in Sports. Organised by International Society of Biomechanics in Sports. Perth, Australia.

Giakas G, V Baltzopoulos and R M Bartlett (1998). Improved extrapolation techniques in recursive digital filtering: a comparison of least squares and prediction. Journal of Biomechanics 31(1), 87-91.

Giakas G and V Baltzopoulos (1997). A comparison of automatic filtering techniques applied to biomechanical walking data. Journal of Biomechanics 30(8), 847-850.

Giakas G and V Baltzopoulos (1997). Optimal digital filtering requires a different cut-off frequency strategy for the determination of the higher derivatives. Journal of Biomechanics 30(8), 851-855.

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