6.2 Signals of the Muscles and Motions

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231

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358.1225

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161.5905727

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358.338

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161.7010635

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161.3859179

To achieve improved results of the numerical derivation the measured data of the force

and the joint angle are being smoothed with a moving-average filter with a window

size of ten. Using the gradient() function the first and second derivative of both force

and angle data are calculated. It must be pointed out that the underlying data is dis-

continuous and the numerical derivation will not deliver the exact values of zeros of

the first and second derivatives. There is a need to find the zero values of the derivatives

by an approximate approach. This is done by analysing the values of the derivatives

where a sign change of the values appeared. If a sign change is found the indices of

the points prior in the data arrays are taken and used as approximation of the zero

value of the derivatives. The procedure is shown in the Listing 6.2.2 below.

In the Figure 6.12 (c) the maxima and minima of the joint angle data are found by

means of the numerical derivatives. In comparison with the data of diagram of Fig-

ure 6.12 (b) the approach delivers no unique values of the two stand phases. The nu-

merical second derivative of the joint angle is presented in the Figure 6.12 (d). The num-

ber of inflections is very high despite the smoothing of the discrete measured data. In

the result of the second derivation there is no unique information about the two stand

phases and a further treatment of the data seems too extensive.

In the treatment of the force data the first and the second derivation deliver many

zero values in the first 1.5 seconds of the data Figure 6.12 (e and f). In comparison with

the findpeaks() function (a) the first and second derivative of the force data deliver

some more significant maxima and minima in the course of the signal. Finally, both

approaches yield no unique information about the second and third stand phases of

the 3 knee bends.

Third approach

In a third approach a threshold method is used to determine the points of interest. The

application of thresholding to determine trigger points in force and knee joint angle

data has already been proven successfully [69]. The method is explained by means of

the force data.To get the threshold value an average over the force values is calculated

and then multiplied with a factor of 95%. All force values above the threshold are

set to NULL. With the find() function the indices of all elements unequal to zero are