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\section{Theory}  \subsection{wave speed in non-coronary arteries}  The direct measure measurement  of local wave speed by the foot-to-foot method, i.e. measuring time of travel of the foot of a waveform between two measurement sites a known distance apart, is practically problematic. problematic in practice.  The wave speed varies with axial distance along an artery because of anatomical and structural changes in the artery wall and so the 'local' wave speed must be measured over relatively short distances. Small distances between measuring sites means that travel times are small and it is difficult to make measurements with sufficiently high temporal resolution with currently available transducers. 'Wave speed' measured clinically by the foot-to-toot method are actually some average measure of the wave speed over very large distances, typically carotid-to-femoral, and are not good estimates of the local wave speed at a particular location. Local wave speed is usually measured by the simultaneous measurement of pressure and velocity (or volume flow rate). The measurement of the local characteristic impedance, which is related to the local wave speed, involves averaging the impedance $Z = \overline{P}/\overline{Q}$ over a certain range of harmonics, where $\overline{P}$ and $\overline{Q}$ are the Fourier transforms of the measured pressure, $P$, and flow rate, $Q$. [ref. Segers]