Linear interpolation on an infinite grid of knots separated by equidistant intervals δq. Each knot n in the comoving frame (top line) is interpolated on the [m,m + 1) interval in the inertial frame (bottom line). The integer shift s = m−n defines how many δq intervals the comoving grid is Doppler-shifted with respect to the inertial grid. The l.h.s. 4 and r.h.s. 1 −4 weights are indicated by sloped solid and dotted lines. The weight 4 is determined by the remainder r = q_μ + q [ n] −q [m], which is the frequency displacement between the inertial knot m and its related comoving knot n.