Frequency analysis for filtering kinematics data

[Jonathan Sinclair]

Hi All

Just a quick question about frequency cut-off for filtering.

I often see in papers that investigate kinematics the authors have established an appropriate cut-off frequency using Fast fourier transform of the data as the frequency at which 95% of the signal power is below.

How is this typically accomplished and on what marker(s).

Any help would be appreciated

Jonathan

[Keri Collins]

Re: Frequency analysis for filtering kinematics data

Any waveform that deviates from a sinewave will have harmonics (components at other frequencies) and an FFT will tell you what these frequencies are. I have used FFTs to tell me the frequency components of signals derived from kinematics data (position of a part that *should* have been moving sinusoidally through time).

As an example for here, I created a sawtooth wave, which is rich in harmonics, at 1.5 Hz in MATLAB.



The fft of this wave shows a main energy peak at 1.5 Hz (with a value of 0.6) and the other harmonics after this, with lower energy. It's a bit scrappy as I only used 10 cycles for the analysis.



If you wanted to discard the higher frequencies, you could delete (set to zero) anything that had an energy below 95%x0.6 and then perform an inverse fourier transform (which also can be done in MATLAB) to look at the original waveform with the higher harmonics removed.

You might also consider using a low-pass or bandpass filter, or if you just wanted to smooth the data something like LOESS (locally weighted scatterplot smoothing) could be used, and these are all available in MATLAB (may need the signal processing toolbox though).

If you don't use MATLAB Excel 2010 has FFTs in its Analysis ToolPak (which you may need to load - check the help file for details) but I haven't used it.

I hope this helps.

[Jenna Yentes]

Re: Frequency analysis for filtering kinematics data

Jonathan,

There are actually several sources for finding this information. First of all, you have to decide what filtering best fits your research question. For standard gait analysis, a very popular algorithm used for filtering data is the Jackson algorithm. (Jackson KM. Fitting of mathematical functions to biomechanical data. IEEE Transactions on Biomedical Engineering. 1979; 26(2):122-4) This algorithm states that a different cutt-off frequency be used for each marker. In David Winter's book, Biomechanics and Motor Control of Human Movement, there is a really nice section on filtering data (chapter 2, I think). Another really good chapter on signal analysis can be found in a book edited by Nick Stergiou, Innovative Analyses of Human Movement. The last chapter explains, very simply, power spectrum analysis and filtering. Last, for the light hearted, there is a great book on Fourier Transforms called Who is Fourier? A Mathematical Adventure. It is a "cartoon" style book but makes this somewhat complicated math very easy to digest.

I hope this will give you some additional resources.

Jenna

[Jonathan Sinclair]

Re: Frequency analysis for filtering kinematics data

Thanks to you both this has been a big help. Jenna - i'd just ordered a copy of Stergiou's book it arrived yesterday and it's excellent a great recommendation.