We have studied the early time evolution of granular segregation patterns in a horizontal rotating cylinder partially filled with a sand-salt mixture. The growth of concentration fluctuations starting from premixed initial conditions was analyzed using Fourier techniques. In one mixture; we observed generally merging dynamics in the segregated bands up to the onset of saturation. At the threshold of saturation; we found a spectrum of wavelengths with a broad peak. The peak position was nearly independent of the tube rotation rate. The overall growth rate of Fourier modes had a maximum at a particular value of the angular rotation frequency. In a slightly different mixture; we observed transient traveling waves when the larger grains were in the majority. We measured the wave speed as a function of several parameters using presegregated initial conditions to launch waves of various wavelengths.