Let V(0, t) denote the voltage at position zero and time t. If we represent our input V (0, t ) as a sum of sinusoids using a Fourier transform, all these sinusoids will propagate along the transmission line at the same speed, so that their sum will remain undistorted as it propagates, and we will have our ideal transmission line: V ( x, t ) = V (0, t − τ) with τ = x √( LC ).