Sampled Traveling-Wave Solution

As discussed in detail in Appendix G, the continuous traveling-wave solution to the wave equation given in Eq. (4.2) can be sampled to yield

$$y(nT,mX) = y_r(nT-mX/c) + y_l(nT+mX/c) \mbox{(set $X=cT$)}$$

$$= y_r(nT-mT) + y_l(nT+mT)$$

$$\isdef y^{+}(n-m) + y^{-}(n+m) \protect,$$ (5.3)

where $T$ denotes the time sampling interval in seconds, $X=cT$ denotes the spatial sampling interval in meters, and $y^{+}$ and $y^{-}$ are defined for notational convenience.