The next filtering approach evaluated was MATLAB®via its function “filtfilt”. As stated in the MATLAB®documentation, “filtfilt minimizes start-up and end transients by matching initial conditions. . .” Using a 10 kHz cutoff frequency with filtfilt, Fig. 19.7 (dashed lines), appears to have created much improved results that do not suffer from the end-effects that were found with the previous Mathcad®filtering approach (with no end-effect minimization). The filtered results still show some low-frequency oscillations, so in an attempt to remove these the raw data was filtered using a 3 kHz cutoff frequency. This result shown in Fig. 19.8 (dashed lines) is indeed smoother, but has a strange enddistortion on the right side again. The cause of this distortion is related to limitations in MATLAB®’s filtfilt end-effect minimization technique. The way filtfilt attempts to match initial conditions and minimize start-up and end transients is by copying a small section of data from each end of the original data and placing a flipped mirrored version of it onto each end. The length of these artificial copies is related to the number of filter coefficients used in the filter. The idea is that with such extensions and performing filter-precharging after each filter pass of the bi-directional filter, the filter will hopefully yield reasonable results. With a 10 kHz cutoff frequency, the algorithm performed well (Fig. 19.7), but with a 3 kHz cutoff frequency, the algorithm appears to “break down”. The problem seen in Fig. 19.8 is caused by the time delay from each filter pass being larger than the filtfilt data extensions. More details on the causes of this type of distortion are found at [8]. 0.1 0.05 0 400 300 200 100 0 400 Raw Filtered Raw Filtered 300 200 100 0 0 0 2x10−4 4x10−4 Time [s] Time [s] Raw Displacement [in] Filtered Force [lfb] Filtered Displacement [in] Raw Force [lfb] 6x10−4 8x10−4 0 2x10 −4 4x10−4 6x10−4 8x10−4 0 0.05 0.1 Fig. 19.7 Force–time (left) and displacement–time (right) responses with MATLAB ® 10 kHz filtered responses (dashed lines) 0.1 0.05 0 400 300 200 100 0 400 Raw Filtered Raw Filtered 300 200 100 0 0 0 2x10−4 4x10−4 Time [s] Time [s] Raw Displacement [in] Filtered Force [lfb] Filtered Displacement [in] Raw Force [lfb] 6x10−4 8x10−4 0 2x10 −4 4x10−4 6x10−4 8x10−4 0 0.05 0.1 Fig. 19.8 Force–time (left) and displacement–time (right) responses with MATLAB ® 3 kHz filtered responses (dashed lines) 158 W.J. Briers III
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