Objectives. Some Basic Terms. Analog and Digital Signals. Analog-to-digital conversion. Parameters of ADC process: Related terms
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1 Objectives. A brief review of some basic, related terms 2. Aalog to digital coversio 3. Amplitude resolutio 4. Temporal resolutio 5. Measuremet error Some Basic Terms Error differece betwee a computed ad true value; ofte used to reflect the accuracy of a measuremet Reliability the extet to which a measuremet procedure yields the same results o repeated trials; sometime associated with precisio Validity the extet to which a measuremet procedure measures what it is supposed to measure Resolutio The fieess of detail that ca be distiguished i a measuremet Aalog ad Digital Sigals Sigal: a fluctuatig electric quatity (e.g., a voltage) whose variatios represet coded iformatio Aalog-to-digital coversio Aalog sigal: represets data via a cotiuously variable quatity Digital sigal: represets data via discrete variable quatities aalog sigal ADC digital sigal computer memory Related terms Digitizatio the process of covertig a aalog sigal ito digital form Aalog-to-digital coverter (ADC) a device that digitizes a aalog sigal Samplig a aalog sigal is said to be sampled to produce the digital sigal Quatizatio to subdivide ito small, measurable icremets; digital sigals are limited by the umber of biary digits ( bits ) that ca be used to represet them Parameters of ADC process: Iput rage: voltage rage to be detected bipolar: V, 5V, or V commo i our lab uipolar: -V, -5V, -V this parameter is ofte selectable i hardware or software System gai: degree of sigal amplificatio prior to samplig
2 Parameters of ADC process: Amplitude resolutio: how precisely the sigal amplitude ca be quatified determied by bit value of ADC commo: 2-bit (2 2 = 496 discrete levels) 6-bit (2 6 = 65,536 discrete levels) Temporal resolutio: how frequetly the ADC samples the aalog sigal determied by samplig rate values from 3 to 2 are commo i our lab Amplitude ad temporal resolutio greatly affect the quality of the digital sigal +5 V V -5 V Amplitude Resolutio A 4-bit A/D set up (2 4 = 6 discrete levels) biary values Amplitude Resolutio A 4-bit A/D set up close-up view V 3.75 V 3.25 V 2.5 V.875 V How precisely ca a 2-bit ADC detect amplitude chages i a aalog sigal? 2 bit ADC = 2 2 = 496 discrete levels over iput rage V iput = rage of 2 V (2 V) / (496 ADC uits) =.49 V per ADC uit Is 4.9mV per ADC uit good resolutio? It depeds. For example, if a force plate equates + V to 25 N, the ADC uit represets.22 N. This meas you caot detect force chages <.22 N. ADC Temporal Resolutio Samplig Rate: how ofte is the sigal sampled? t t 2 t t 3 Samplig period: time betwee adjacet samples e.g. = t 2 t Samplig rate (f ): frequecy with which samples are take e.g. f = / ADC Temporal Resolutio What is a adequate samplig rate? Govered by Shao s samplig theorem: the sigal must be sampled at a frequecy at least twice as high as the highest frequecy preset i the sigal itself This miimally acceptable samplig frequecy is kow as the Nyquist frequecy But, how ca we kow what the sigal frequecy cotet of a sigal is? 2
3 COM Positio (mm) Jumpig VGRF (N) Racket Positio (mm) But, what does frequecy cotet mea? What do you thik the frequecy cotets of these sigals are? GA EMG (V) Fourier Aalysis Frequecy cotet of a sigal ca be objectively determied via a Fourier aalysis Fourier discovered that ay sigal, o matter how complex, ca be represeted by a ifiite sum of sie ad cosie waves y ( t) A B si f t C cosf t I practice, a fiite umber of frequecies ca adequately represet a sigal. The Fourier trasformatio allows the frequecy compoets of a sigal to be revealed. The Fourier Trasformatio Coverts a sigal from a time domai to a frequecy domai by separatig sigals ito sie waves of differig frequecies that sum to equal the origial waveform. The Power Desity Spectrum is the result of iterest Power Desity Spectrum.5 Time Domai Frequecy Domai Power Desity Spectrum origial sigal 2 oise added Power Desity Spectrum Raw EMG sigal Power Spectral Desity time (s) time (s) frequecy () frequecy () 3
4 Frequecy Cotet Prevalet frequecy cotet of some commo biomechaical sigals (leared via FFT): ADC Temporal Resolutio Now, back to samplig rate: What if you violate Shao s samplig theorem? Activity Stadig (motio) Walkig (motio) Ruig (motio) Heelstrike trasiet (GRF) Surface EMG Idwellig EMG Max Freq of Iterest A error, kow as aliasig, will occur, corruptig your data Frequecies greater tha ½ the samplig rate ca distort the recorded sigal A 4 sigal, so Nyquist Frequecy is 8 aalog 5 4 sie wave Aother example 25 Aliasig occurs at samplig rate of sigal appears to be.33 Samplig Rate Typical samplig rates used to collect various sigals i biomechaics: Sigal Motio Force Surface EMG Idwellig EMG Typical SR Measuremet Errors No measuremet process is perfect: there will always be some degree of error i the data Measuremet errors fall ito two categories Radom Errors Systematic Errors Both ca be atteuated (miimized), but either ca be completely elimiated Radom errors may be reduced through data processig techiques. Systematic errors geerally ca ot. Oe way to reduce systematic error is to be overly careful durig the data collectio process. 4
5 Radom Error - Example 3 people measure the distace betwee two lies that are.5 cm apart Systematic Error - Example perso measures a distace betwee two lies that is.5 cm apart, but places the ruler dow icorrectly cm.4 cm.6 cm They do t all get the same value, but this radom fluctuatio ca be largely elimiated by averagig the three values ( ) / 3 =.5 cm.2 cm.2 cm.2 cm This idividual was cosistet i his/her measuremets, but he/she has itroduced a systematic error ito the data No amout of processig ca remove this error Examples Systematic Errors: Poor placemet of aatomical markers Movemet of markers/ski relative to boes Digitizatio errors (some) Radom Errors: Digitizatio errors Marker jigglig/vibratio Electrical iterferece Miimize Measuremet Error Use cosistet, proper techiques for data collectio; use a checklist ad data collectio log to esure cosistecy Properly trai your persoel Use of high quality equipmet Be careful! Summary Some basic terms: error, reliability, validity ad resolutio, Aalog to digital coversio Amplitude resolutio Review: the sie fuctio y ( t) A B si f t A the mea offset from zero B the amplitude of the sigal f the frequecy of the sigal A = B = f = Temporal resolutio Fourier Aalysis Radom ad Systematic Error 5
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