DESIGN AND DEVELOPMENT OF MEDICAL ELECTRONIC ...

SPECTRAL ANALYSIS 245Figure 5.21 A hybrid two-dimensional spectral estimator: Spatiotemporal data (a) are transformed along the time domain into an intermediatearray (b) through the application of a windowed FFT to every row of the original data. Applying an AR PSD estimator to every columnof the intermediate array completes the two-dimensional PSD estimation process (c). [Reprinted from Med. Eng. Phys., 17, D. Prutchi,A High-Resolution Large Array (HRLA) Surface EMG System, pages 442–454, 1995, with permission from Elsevier.]an intermediate transform G int ( f, r) is computed by applying the FFT along each row (timedomain) of appropriately weighted data. The two-dimensional spectral estimate G( f, k) isthen completed by obtaining the AR-PSD of each column of complex numbers in the intermediatetransform. In the more general case, using an array of sensors spread out over anarea, and with a plane wave traveling in any direction under the array, a three-dimensionalhybrid spectral estimator can determine not only the wave’s components and their velocitiesbut also each component’s bearing.A practical example of the use of this method is the analysis of biopotentials that canbe picked up from skeletal muscle fibers using electrodes attached to the skin [Prutchi,1994, 1995]. These biopotentials are caused by the sum of currents from action potentialsthat travel down individual muscle fibers responsible for the contraction of muscles. Theconduction velocity, as well as the origin of these potentials, contains a wealth of informationthat can be used, for example, as an aid in the early diagnosis of nerve and musclediseases. The large number of convoluted signals and the very small differences betweentheir waveforms make it impossible to determine this information from spatiotemporaldata (Figure 5.22b) recorded differentially using 32 surface electrodes placed 2.54 mm