Digital Imaging Laboratory & Pulse Oximetry Laboratory Report

Transcription

1 Digital Imaging Laboratory & Pulse Oximetry Laboratory Report January 14, 2016 ES4C5 Optical Engineering Assignment - Dr D.D.Iliescu & Professor D.P.Towers

2 Contents 1 Digital Imaging Laboratory Normalised Contrast Transfer Function and Spatial Frequency Definitions Spatial Frequency and CTF Printer Resolution Measurement Pinhole Fabrication Tolerance Measurement and Magnification True Magnification Imaging and Measurement of CCD chip Target Object Pulse Oximetry Laboratory Report Operating Principles and Applications Experimental Procedure Discussion of Results Recovering a Corrupted Heart Beat Signal Tissue Attenuation List of Figures 1 Microscope captured image of USAF1951 test target Plot showing grey values horizontally across Group 2, Element 1 of the USAF1951 Test Target at low magnification Plot showing grey values vertically across Group 5, Element 1 of the USAF1951 Test Target at low magnification Contrast Transfer Function against Spatial Frequency ISO test chart Drawn by Stephen H. Westin - Cornell University Microscope captured images comparing the horizontal and vertical printer resolution limits captured at low magnification Pinhole of unknown dimensions and manufacturing tolerances Microscope captured images of an LCD monitor display Microscope captured image of CCD taken at high magnification Red and infrared scaled alternating current (AC) signals at different arterial oxygen saturation (S a O 2 ) points of 0%, 85% and 100% (Wukitsch et al. 1988) Schematic of equipment used to capture pulse oximetry data Plethysmograph of seated and rested participant A Plethysmograph of participant A shortly after a burst of exercise Plethysmograph of a seated and rested participant B Plethysmograph of a seated but fidgeting participant B, leading to corrupted data From bottom left clockwise: a) Original user corrupted signal. b) corrupted signal in the frequency domain following Fourier transform. c) unwanted frequencies eliminated leaving expected frequencies behind. d) reverse Fourier transform yields filtered data Pleth signal when blood flow is restricted at the wrist Pleth signal comparison between hand down and hand raised positions in red and blue respectively Pleth signal comparison between different fingers on the same participant OEMIII Data Specification

3 1 Digital Imaging Laboratory 1.1 Normalised Contrast Transfer Function and Spatial Frequency Definitions The modulation transfer function is a measure of the performance of a microscope. In real terms it describes how well the microscope reproduces the image of the subject which it is trained upon. Images obtained from any imaging device will be degraded somewhat due to optical imperfections and aberrations. The contrast or Modulation can be expressed Modulation = I max I min I max + I min, (1) where I max and I min are the maximum and minimum measured intensities from a repeating object respectively. Repeating patterns generate sinusoidal intensities that vary in accordance with spatial frequency usually and thus are used to measure the contrast and MTF of an image. Modulation of the image is expected to be less than that of the subject, the degree to which differs in as a function of spatial frequency and therefore MTF is defined as a ratio of the two such that MT F = Image Modulation/Object Modulation (2) In the digital imaging laboratory, it is assumed that object modulation 1 and thus equation (2) reduces to MT F = Modulation. The normalised contrast transfer function (CTF) is equivalent to MTF when imaging periodic black and white lines such that CT F = MT F = I max I min I max + I min. (3) Calibration of the digital microscope is performed with the use of a precise artifact such as a precision pinhole and a calibration factor. At a given magnification and a given focal length, the calibration factor (CF) is determined by measuring the number of pixels across the diameter of a known pinhole such that CF = no. pixels diameter. (4) The size of objects and artifacts in subsequent images at a similar magnification and focal length can be measured using the reverse equation, Size = no. pixels. (5) CF whilst noting that calibration factor is limited to a specific magnification and focal length. calibration factors are established for different magnifications. Different Spatial Frequency and CTF The USAF1951 test target, as shown in figure 1, is a standardised piece of measuring equipment used to test optical imagine equipment. In this particular application it may be used to determine the spatial resolution of the camera with the help of table 1. Images of the test target are captured using the Veho Discovery USB microscope at both high and low magnifications. 2

4 Figure 1: Microscope captured image of USAF1951 test target Group Element Table 1: Number of Line Pairs/mm in USAF Resolving Power Test Target Post processing software ImageJ is used to gather contrast data from the USAF1951 test target for differing scales of the line sets. Figure 2 shows the contrast plot of group 2 element 1 of the test target, measured horizontally at low magnification. It is noted that the camera reliably resolves the lines which correspond to a spatial resolution of 4 line pairs per mm. The USAF1951 test target features lines for establishing vertical and horizontal resolution, however no appreciable difference between horizontal and vertical resolution can be discerned and thus data from one orientation is presented in this report. 150 Grey Value Distance (pixels) Figure 2: Plot showing grey values horizontally across Group 2, Element 1 of the USAF1951 Test Target at low magnification. 3

5 The microscopes spatial resolution is the limit at which objects can no longer be distinguished from each other. Images captured by the microscope of the test target reveal that at low magnification the test target object in group 5, element 1 is barely resolved, as seen by the data in figure 3. According to the look up data in table 1, this corresponds to a spatial resolution of 32 line pairs per mm Grey Value Distance (pixels) Figure 3: Plot showing grey values vertically across Group 5, Element 1 of the USAF1951 Test Target at low magnification. Similarly, the spatial resolution at a higher magnification reveals that group 7, element 1 of the test target is the limit of the camera s resolving power, which corresponds to a spatial resolution of 128 line pairs per mm. It is therefore concluded that spatial resolution increases with magnification, although more data should be collected at different magnification levels to validate this conclusion. Multiple measurements of CTF are made for different elements of the USAF1951 test target and are plotted against the spatial frequency data found in table one. The resulting plot, shown as figure 4. It is observed that spatial frequency is inversely proportional to CTF. 0.8 CTF Spatial Frequency (Lines per mm) Figure 4: Contrast Transfer Function against Spatial Frequency. 4

6 1.2 Printer Resolution Measurement The ISO standard for measuring camera resolutions is the ISO12233 test chart, shown in figure 5. Figure 5: ISO test chart Drawn by Stephen H. Westin - Cornell University. As seen in figure 6, the printer appears to exceed its reliable resolution capacity after the seventh graduation marker both horizontally and vertically. As indicated by the ISO12233 test chart, this corresponds to lines per picture height. The picture height for the measured printed chart is 72mm, thus the printers resolution in lines per mm (L/MM), can be expressed: L/MM = V alue 100 P ictureheight = = (6) 72 A more widespread way to express printer resolution is in dots per inch (DPI). L/MM is multiplied by 2 to establish a value for line pairs per mm (LP/mm) and further multiplied by 25.4 to establish line pairs per inch which is analogous to DPI. Thus DPI may be found using the formula: DP I = LP/mm 25.4 = L/mm = = 494dpi. (7) (a) Horizontal printer resolution limit. (b) Vertical printer resolution limit. Figure 6: Microscope captured images comparing the horizontal and vertical printer resolution limits captured at low magnification. 5

7 Purportedly the printer performance should be in the region of 600dpi, thus it is suggested that the manufacturers claims are ambitious. However other factors should be taken into consideration for example: the quality of the ink used; the age and wear of the printer; the cleanliness of the printer heads; the quality of paper used for printing. Indeed, it is indicated that the printer was in operation in economy mode, which may negatively impact the print resolution due to the reduction in ink usage and increased print speed. 1.3 Pinhole Fabrication Tolerance A pinhole of unknown manufacturing tolerances can be measured with a certain degree of accuracy by measuring the width in pixels of a known artifact and establishing a calibration factor. The artifact used to establish a calibrating factor is a 200µm pinhole manufactured by Edmund Optics to a manufacturer stated tolerance of ±5µm. Images are taken of the 200µm pinhole and with the use of the post-processing tool ImageJ, the hole is carefully measured. Multiple measurements establish the size of the hole in pixels to be an average of pixels ±1 at the higher magnification level. The calibration factor is calculated using equation (4): CF = ± 1 = ± 35. (8) 0.2mm ± The manufacturing tolerance of the pinhole of interest (figure 7) can be approximated as the difference between the maximum and minimum diameters measured. It is not possible to speculate beyond this as the original manufacturing tolerances are not known but errors made in measurement of the unknown pinhole demonstrate the errors associated with the equipment used. The unknown pinhole is measured (a) Pinhole of interest at low magnification. (b) Pinhole of interest at high magnification. Figure 7: Pinhole of unknown dimensions and manufacturing tolerances. in the ImageJ software at multiple angles revealing a maximum diameter of 1180px ±1 and a minimum of 1125px ±1 giving a maximum diameter of 55 ±2 pixels. Using equation (5) this measurement is converted into to a size such that diameter = 55px ± 2 = 45.6µm ± 3.0µm. (9) ± 35 The average diameter of the unknown pinhole is found to be pixels, which equates to 951µm and it is estimated that it was manufactured to a tolerance of 22.8µm ± 1.5 ( diameter/2). This conclusion 6

8 assumes that the effects of wear and tear are negligible. It additionally assumes that deviations from the desired set-point at the point of manufacturing would manifest as disparity in diameter around the hole which is a not always the case: a perfectly round hole may still be manufactured to loose tolerances depending on the application. 1.4 Measurement and Magnification An attempt is made to measure the pixel size of the Iiyama monitors found the Warwick Engineering s computer suite. Measuring many of a repeating object and dividing by the number measured will generally yield a more accurate result than measuring the object directly. It would therefore appear prudent to attempt to measure pixel size using the lowest magnification, however, as discussed in section 1.1, the resolving power of the microscope increases with increasing magnification. Two images are collected of the Iiyama LCD monitor, one at low magnification (figure 8a) and one at high magnification (figure 8b). A calibration factor for both high and low magnifications is established with the 200µm pinhole using the formula CalibrationF actor = P ixels/length. Using a low magnification, 34 pixels were calculated to measure a total of 8.730mm, rendering an individual pixel width of 0.257mm. Using a high magnification just 7 pixels were calculated to measure 1.806mm rendering an individual pixel width of 0.258mm. Both values are surprisingly similar indicating that the higher degree of accuracy (a) Pinhole of interest at low magnification. (b) Pinhole of interest at high magnification. Figure 8: Microscope captured images of an LCD monitor display achieved by measuring more pixels at a lower magnification is offset by the increased resolving power and clarity of higher magnifications. Assuming that the 24 display conforms to a 16:9 aspect ratio as per the manufacturers specification, the width of the screen is computed to be 531.3mm, giving each of the 1980 pixels an actual width of 0.268mm. This result points,although not significantly, to the high magnification method being more accurate. Indeed, it appears that for the measurement of non-repeating and repeating artifacts, higher magnification will give similar or improved results in accuracy over a lower magnification. 7

9 1.4.1 True Magnification True magnification, defined as M = Image Size Object Size, (10) is discerned by comparing the known object size with the size of the image cast upon the CCD inside the microscope. For the sake of continuity, the LCD pixels are used as test objects to measurements are used to calculate true magnification. Assuming a sensor size of 6mm x 5mm and an image captured at 640x480 (VGA), the size of the image in the horizontal, is expressed Image size = test object size (pixels) 640 CCD length. (11) In figure 8a, at the lower magnification, an LCD pixel measures 18 image pixels. In figure 8b, at the higher magnification, an LCD pixel measures 77 image pixels. Equation (11) thus yields I LowMag = mm = 0.169mm, I HighMag = 77 6mm = 0.722mm. (12) 640 We know from section 1.4 that the real LCD pixel has a width of 0.286mm and thus true magnification is found with the use of equation (10): M LOW = = 0.59, M HIGH = = (13) Although the true magnifications are rather small, the effective magnification is increased substantially when the image cast upon the CCD is viewed on a suitably large monitor. 1.5 Imaging and Measurement of CCD chip Target Object A CCD chip similar in specification to that found within the microscope itself (6x5mm size, 1600x1200 resolution) is imaged in an attempt to measure the physical pixel size. In the case of cameras with a true magnification of 1 or below, it can be generally stated that no CCD can be used to image and measure a CCD pixel of identical specification because the CCD will always require more resolving power and hence more pixels in order to achieve such a task and in-so-doing invalidate the original premise. For the sake of completeness, the resolving power of the microscope as well as that theoretically required are considered. Section reveals that the camera is capable of achieving a true magnification of more than 1 making it plausible to successfully image and measure a CCD pixel. The physical pixel dimension is 3.75µm x 4.17µm. It is known from section 1 that the spatial resolution of the microscope at its highest magnification setting is 128 line pairs per mm. This spatial resolution determines that the microscope is unable to resolve objects which are smaller than 1/256 of a mm across or 3.91µm. Theoretically the minimum spatial resolution SR, required to resolve an object of 3.75µm in width can be found using the equation c SR = 1 object to resolve 2 = 1 = 133LP/mm (14) 3.75µm 2 It appears that the microscope is practically capable of resolving an LCD pixel vertically, since 3.91µm is 8

10 Figure 9: Microscope captured image of CCD taken at high magnification. smaller than the LCD pixel height, however this is not the case: no pixels can be observed upon inspection of the images. It is suggested that the primary reason for this is lack of contrast between the pixels themselves. Lines on a test chart like USAF1951 are substantially easier to resolve than low contrast artifacts. Secondary reasons such as surface scratches on the CCD scattering the light from the microscopes LEDs; difficulty in focusing; and the glass layer of the CCD distorting the pixels themselves may be contributory. 2 Pulse Oximetry Laboratory Report 2.1 Operating Principles and Applications Pulse oximetry relies on a pulsating signal generated in arterial blood and the fact that oxygenated hemoglobin 0 2 Hb, and reduced hemoglobin Hb absorb different spectra of light (Jubran 1998). Typically pulse oximeters feature one LED emitting red light at a wavelength of approximately 660nm and another LED emitting infrared at a wavelength of approximately 950nm. Two LEDs emitting different wavelengths are used because oxygenated and reduced hemoglobin exhibit different absorption characteristics at these two wavelengths. At infrared wavelengths, oxygenated hemoglobin (0 2 Hb) absorbs more light than reduced hemoglobin (Hb); at red wavelengths the opposite is true, as observed in figure 10. The arterial blood oxygen saturation (S a 0 2 ) can be compared to the ratio of light absorption from both red and infrared light, allowing empirical calibration of the pulse oximeter. Figure 10: Red and infrared scaled alternating current (AC) signals at different arterial oxygen saturation (S a O 2 ) points of 0%, 85% and 100% (Wukitsch et al. 1988). 9

11 The microprocessor made the pulse oximeter commercially viable, even though the accuracy of different oximeters can differ massively depending on the signal processing algorithm in which they employ. Volunteers are used to calibrate commercial pulse oximeters and thus the accuracy is limited by the safe range of oxygen saturation that volunteers can be exposed to (Ralston, Webb, and Runciman 1991). Aside from measuring blood oxygen saturation almost all commercially available pulse oximeters can output plethysmographic data to measure pulse rate. The introduction of pulse oximeters has seen significant improvements in the detection of hypoxemic (arterial saturation S p O 2 < 90%) patients (Cullen, Nemeskal, and Cooper 1992) and a reduction of of unanticipated admissions to intensive care during anesthetisation (Moller, Johannessen, and Espersen 1993), among many other improvements. 2.2 Experimental Procedure A Nonin Xpod cable oximeter is used to measure oxygen saturation S p O 2 and pulse. The oximeter outputs red light at 660nm and infrared at 910nm and claims to be between 70% and 100% accurate. The experiment makes use of a Nonin OEMIII data processing chip which outputs data to a computer running OEM2 software. Figure 10 shows the layout of components used. Figure 11: Schematic of equipment used to capture pulse oximetry data. The experiment consisted of four patients, two females and two males. One female participant had a broken arm and one male participant was recovering from a night of intoxication. Data was captured using the Xpod cable oximeter of all participants at rest. Subsequent data was collected from other participants following exercise and using different fingers, different arm positions. Errors are managed by instructing participants to remain motionless during the approximately 20 second data capture process and by using the same finger when comparing resting data against post-exercise data etc. Further data is captured to establish the effect of motion on the data produced. Data is collected in the OEM2.exe application and exported as Comma Separated Value (.CSV) files. These files are read into Matlab using the xlsread() function and pleth data may be plotted using the Matlab script which can be found in the appendix. Heart rate data may be captured in a similar way, although it is important to note that heart rate data can only be extracted by selecting the correct interval within each packet (25 data points) of data from the.csv file. but the first few pieces of data collected are not necessarily the beginning of a packet. 10

12 2.3 Discussion of Results Two participants are compared. Ten seconds of data is shown in the following figures as 75 data points equate to a second. Figure 12 is a plot of the plethysmographic data from participant A at rest, figure 13 shows the same participant following a short intense bout of exercise running up stairs. Figure 14 shows a different individual, participant B at rest. Table 2 displays beat to beat time intervals for the same participants and data sets, whilst table 3 shows the beat to beat heart rate, average heart rate and heart rate variability (HRV). Figure 12: Plethysmograph of seated and rested participant A Figure 13: Plethysmograph of participant A shortly after a burst of exercise Figure 14: Plethysmograph of a seated and rested participant B 11

13 Beat A post-exercise A at Rest B at rest Avg σ σ Table 2: Beat to beat time interval of participant A at rest and after exercise and participant B at rest. Beat A post-exercise A at Rest B at rest Avg σ σ Table 3: Beat to beat heart rate (HR) of participant A at rest and after exercise and participant B at rest. At rest, participant A exhibits a heart rate average of 95 beats per minute (BPM) which appears to be high. It was observed that some participants seemed excitable during resting measurements. A higher 12

14 resting heart rate may also be indicative of lack of fitness, a hangover or illness. Curiously, heart rate variability (HRV) is proportional to fitness and thus despite participant A having a higher resting heart rate than participant B, participant A s HRV is higher, indicating that the result might not be an issue of fitness. Unsurprisingly, following a brief bout of intense exercise participant A s heart rate increases substantially to an average of 157BPM over the data capture period. This increase in heart rate is coupled with a reduced range of pleth data: at rest, participant A s pleth signal varies between around 50 to 200 whereas post-exercise the signal varies between 80 to 130. This reduction in range by a third indicates that the heart is pumping less blood per stroke than at rest. Participant B at rest has an average heart rate of 57BPM which puts him/her in the normal range for a resting heart rate. It is noted that the data collected from this test exceeds the maximum pleth signal range, which may introduce an error in the displayed heart rate from the OEMIII module. The instrumental read out of heart rate during the lab was consistently higher than the data suggests and also delayed. The OEM data spec sheet indicates that the display mode heart rate (HR-D on the sheet found in the appendix) calculates a four beat exponential average which explains the latency in HR read out. Both figures 12 and 14 feature some data irregularities. It is suggested that both participants may have altered themselves or the position of the pulse oximeter on their finger during the experiment thereby introducing potential errors in the OEMIII read out. The data is not corrupted excessively and is still easily to interpret implying that some movement during measurement is acceptable, but a potential source of error nonetheless. 2.4 Recovering a Corrupted Heart Beat Signal The oximeter is highly sensitive to movement of the patient which can render data unreadable both by humans and by the OEM data processing unit. The data shown in figure 15 was captured whilst the patient intentionally moved their finger in rapid motions. It is possible to apply filtering to the signal particularly to maintain clear peaks in the data so that processing software can identify peaks and quickly relay the information to the patient in real time. Generic smoothing algorithms such as Savitzky-Golay filtering make the data appear less noisy, however they often leave pre-existing rogue peaks which introduce measurement errors. A better option is to use Fourier smoothing to remove unwanted frequencies from the data. This approach is particularly powerful because an expected frequency can be determined from the heart rate of the patient, and frequency cut-offs may be established around this value. Fast fourier transform filtering is made possible with the use of Matlab. The process behind FFT filtering is mathematically complicated and fortunately Matlab abstracts much of the complication away from the user. FFT filtering may be explained by the following steps: Raw data is sampled at a predetermined frequency. (75 is prudent for this application as 75 data 13

15 Figure 15: Plethysmograph of a seated but fidgeting participant B, leading to corrupted data Figure 16: From bottom left clockwise: a) Original user corrupted signal. b) corrupted signal in the frequency domain following Fourier transform. c) unwanted frequencies eliminated leaving expected frequencies behind. d) reverse Fourier transform yields filtered data. points equates to one second.) Fourier transform is computed to convert from the time to frequency domain Frequencies outside of the expected range are eliminated, much like a high and low pass filter. Frequencies to eliminate are decided upon based on the frequency of the input heart rate. For example, 60BPM equates to 1Hz, 120BPM equates to 2Hz etc. 14

16 Reverse Fourier is applied to convert the data back into the time domain. The results of the aforementioned method are shown in figure 16. It is notable that this method is highly dependent on the correct elimination of frequencies: removing the wrong range of data can alter the apparent frequency of the filtered data, rendering the result useless. 2.5 Tissue Attenuation Attenuation is a measure of intensity loss due to transmission through a medium. In the case of pulse oximetry, the attenuation of the skin can alter the pleth signal and therefore introduce a source of error that must be compensated for. For example, as noted by Feiner, Severinghaus, and Bickler (2007), light attenuation is problematic for persons with a dark skin pigmentation. A method by which to estimate the attenuation of the skin is to intentionally restrict blood flow to the hand, thereby reducing the effect of pulsatile blood flow on the pleth signal to establish a minimum value. Restriction of blood can be achieved by raising the hand as high as possible above the heart, thereby reducing pressure or by manually blocking blood flow through the wrist with pressure. Figure 17 shows the effect of blocking blood flow to the hand by clamping the wrist. It is observed that a pulse reading is no longer discernible and a minimum pleth value of 100 is maintained throughout. It is questionable whether or not this represents a minimum because by clamping the wrist, blood is forced into the hand at an unusually high pressure, which may offset the result. Figure 17: Pleth signal when blood flow is restricted at the wrist. Figure 18 shows the effect of hand below and above the heart. It is observed that the pleth signal intensity drops as expected as the hand is raised, but not appreciably, and the presence of pulsatile blood is still highly prevalent. A further comparison is made between fingers on an individual participant, as seen in Figure 19. In this instance it is observed that the index finger has the highest attenuation and the little finger, middle and ring substantially lower attenuation. It is speculated that attenuation is higher for the index finger because skin may be thicker on this finger due to disproportionately high use. It is notable that no method was deemed sucessful at determining or estimating attenuation in any meaningful way. It appears that pleth signal varies substantially between different participants, different fingers and different arm positions due to attenuation of the skin. 15

17 Figure 18: Pleth signal comparison between hand down and hand raised positions in red and blue respectively. Figure 19: Pleth signal comparison between different fingers on the same participant. References Cullen, D. J., A. R. Nemeskal, and J. B. Cooper (1992). Effect of pulse oximetry, age, ASA Physical status on the frequency of patients admitted unexpectedly to a postoperative intensive care unit and the severity of their anesthesia-related complications. In: Anesth Analg PMID: , pp Feiner, John R., John W. Severinghaus, and Philip E. Bickler (2007). Dark Skin Decreases the Accuracy of Pulse Oximeters at Low Oxygen Saturation: The Effects of Oximeter Probe Type and Gender. In: International Anesthesia Research Society Jubran, A. (1998). Pulse Oximetry. In: Tobin MJ (ed). Principles and Practice of Intensive Care Monitoring. doi: /s , pp

18 Moller, J. T., N. W. Johannessen, and N. W. Espersen (1993). Randomized evaluation of pulse oximetry in 20,802 patients: II. Perioperative events and postoperative complications. In: Anesthesiology 78. PMID: , pp Ralston, A. C., R. K. Webb, and W. B. Runciman (1991). Potential errors in pulse oximetry. In: Anaesthesia doi: /j tb09410.x, pp issn: Wukitsch, Michael W. et al. (1988). Pulse oximetry: Analysis of theory, technology, and practice. In: Journal of Clinical Monitoring 4.4. doi: /bf , pp issn: Appendix Matlab code used to extract Pleth Data 1 f u n c t i o n []= p l e t h E x t r a c t 2 x = input ( Input F i l e number :, s ) 3 4 plethvect=x l s r e a d ( s t r c a t ( SPO, x,.csv ),1, D2 : D750 ) ; 5 timevect =[1: s i z e ( plethvect ) ] ; 6 7 hfig = f i g u r e ( 1 ) ; 8 s e t ( hfig, P o s i t i o n, [ ] ) 9 p l o t ( timevect, plethvect, r ) x l a b e l ( Sample Number ) ; 12 y l a b e l ( Pleth S i g n a l ) ; Matlab code used to reduce noise 1 f u n c t i o n []= f i l t e r 2 3 hrvect=x l s r e a d ( SPO21145.CSV, 1, D2 : D750 ) ; 4 5 f =75; 6 t s =1/ f ; 7 sz=s i z e ( hrvect, 1 ) ; 8 f r e q D i f f=f / sz ; 9 f=( f / 2 : f r e q D i f f : f /2 f r e q D i f f ) ; 10 time=t s ( 0 : sz 1) ; Low=0.7; High =1.3; p h i l t e r =((Low<abs ( f ) )&(abs ( f )<High ) ) ; 15 hrvect1=hrvect mean( hrvect ) ; 16 one=f f t s h i f t ( f f t ( hrvect1 ) ) / sz ; 17 two=p h i l t e r. one ; 18 hrvect2= i f f t ( i f f t s h i f t ( two ) ) sz+mean( hrvect ) ; % subplot ( 2, 2, 1 ) 23 p l o t ( f, abs ( one ), r ) 24 t i t l e ( U n f i l t e r e d S i g n a l in Frequency Domain ) ; subplot ( 2, 2, 2 ) 27 p l o t ( f, abs ( two ), r ) 28 t i t l e ( F i l t e r e d S i g n a l in Frequency Domain ) ; 29 17

19 30 subplot ( 2, 2, 3 ) 31 p l o t ( time, hrvect, r ) 32 t i t l e ( Raw S i g n a l Data ) ; subplot ( 2, 2, 4 ) 35 p l o t ( time, hrvect2, r ) 36 t i t l e ( F i l t e r e d Heart Rate S i g n a l ) ; OEM Data Specification Figure 20: OEMIII Data Specification 18