4 S. Richardson and M. Richardson TWFs&DFTs When a video is processed in MEscope [8], a rectangular grid of points with rectangular surfaces between them is created. Frames of the video are attached to this surface during animated display of ODS’s extracted from the video. Using a rectangular point grid, millions of pixels in each frame of a cell phone video are processed to extract TWFs for the horizontal & vertical motion of thousands of points in the point grid. Grid points with little or no motion, (like background points), are hidden and their linked TWFs are removed from further analysis. A point grid with background points hidden is shown in Figure 4. ADFTis calculated for eachTWFthat is extracted from the video. Time-basedODS’s are displayed in animation from the TWFs using a sweeping Line cursor. Frequency-based ODS’s are displayed in animation from the DFTs using sine dwell modulation of the ODS at the cursor position. The magnitude & phase of the ODS at selected points can also be displayed, as illustrated in Figure 4. Fig. 4 First-Order ODS Animated from DFTs ODS-FRFs A unique frequency domain function, called an ODS-FRF, can be calculated from each response TWF extracted from a video. A set of ODS-FRFs calculated from the TWFs is typically more accurate because spectrum averaging can be used to reduce extraneous noise from the ODS-FRFs. The magnitude of an ODS-FRF is the APS of the response DOF at a grid point. The phase of the ODS-FRF is the phase of the XPSbetween the response DOFand the DOFof any reference grid point. ODS-FRFs carry the same displacement units as the response TWFs from which they are calculated. But because it is a frequency domain function, an ODS-FRF can be accurately differentiated to velocity units by multiplying it by the frequency variable. Vibration invelocity units is commonly used by vibration analysts to quantify vibration levels in rotating equipment.
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