Measurement Techniques in Biomechanics Lecture 2

1. Measurement Techniques in BiomechanicsLecture 2 August 31th Numerical Methods 1

2. Signal processing • Extract cleaner data • Average waveforms • Correlate to find similarities and differences • Transform into other domains for information

3. Data Smoothing • An attempt to obtain the simplest representation of data that adequately describes an underlying process, while eliminating from consideration data scatter arising from experimental error Wood, 1982

4. A Little BackgroundLinear systems • A system is any process that generates an output signal in response to an input • A system is considered linear if it has 2 mathematical properties • Homogeniety • Additivity • A third property, Shift Invariance, is mandatory for DSP techniques

5. A Little Background Linear Systems have special properties • Commutative • You can add them and order does not matter • Can multiply by a constant • Can multiply by another signal • Synthesis/decomposition * Remember complex signals are a superposition (sum) of simpler signals

6. A Little Background First and Second Order Linear Systems • Order of a system relates to the differential equation needed to define it • First Order (first derivative = velocity) • Second Order (second derivative = acceleration) • Third Order (third derivative = jerk)

7. Some definitions • Derivative • Instantaneous rate of change (slope) • Differentiation • Process of finding the derivative • Integration • Used to measure totality (e.g. volume, area)

8. Finite Difference Techniques • Difference techniques are basically slopes of curves -derivatives • First order systems • Forward finite difference • Two point central difference • Tedious and error prone • Rarely used in processing today due to advent of computers REF Wood pg 315

9. Polynomials • Second order systems of finite difference (acceleration) • Typically parabolic – not linear • Used in a moving average manner (see Fig 4 Wood pg 323) • Are used to approximate underlying biological behaviour • Restricts to lower frequency as it does not go through all points (see figure) • Limits on use on data (see figure)

10. Splines • A number of low order polynomials • Strung together by “knots” • Used for interpolation of data • Kinematic data-missing markers • Rules of thumb • As few knots as possible • No more than one Max/Min (inflection point) • Extreme points should be in center of spline range • No more than a 10-15 point gap*

11. When to use derivatives • Finite differences, polynomials and splines are typically used to smooth clean data • They do not do well with a lot of noise • Can use these for missing data points and for some simple analyses

12. Fourier Smoothing • Convert signal into frequency domain • Choose signal content desired • Reconstruct using only those frequency components (harmonics) • This is a better way to remove noise from signal or to simplify a signal • A better (more common) way however is to filter

13. Digital Filters • Used for 2 general purposes • Signal separation • Needed when a signal has been contaminated (e.g. interference, noise) • Signal restoration • Needed when a signal is distorted (e.g. use of poor equipment)

14. How do digital filters work conceptually • A digital filter allows certain frequencies to pass while others are stopped • Which frequencies are passed depends on what type of filter you are using and the cut off frequency you have set • High • Low • Band • Notch

15. You must know the frequency content of your signal to choose what type of filter to use • You must then determine the Fc • Winter advocates using residual analysis to determine the appropriate Fc • However this only gives you the “bulk” of the signal and therefore f filtered at that frequency you may lose data • Another method to consider is the -3dB mark • A decibal is a logarithmic expression of amplitude • 3dB is half the power of the signal** = .707 of amplitude

16. Some other considerations when choosing a filter • How does the filter performance? • 3 main regions to consider for a filter • Pass band • Stop band • Transition band

17. Frequency Response • Ideally you want a filter: • Fast roll off • No pass band ripple • Good stop band attenuation • Every filter has a • Step response • Frequency response • Impulse response

18. When digital filtering • 3 considerations • Order (higher the order the better frequency magnitude response) • Fc • Type Reference DSP Ch 14 & 21

19. Other numerical methods • Cross correlation • A pearson correlation of two signal that shows you what the signals have in common • This is used a lot in EMG and we will talk more about it then • Spike triggered averaging • Counting the number of spikes in a given time interval • This is used a lot in neurophysiology for motor neuron activity

20. Next Lecture • Transducers and Force measurement • Review of analog to digital conversion (lab 2) • Quantization

21. Group Work • Answer the following question: If a low pass filter is employed at exactly half the sampling rate ( e.g. low pass filter data acquired at 50 Hz Fc set at 25Hz) does this introduce errors into the signal?

22. Group Work • Find examples of cross correlation and spike triggered averaging on the internet • Be able to draw and describe what each process is to the other group • Open for discussion