Climate change, tectonics, and humans create long- and short-term temporal variations in the supply of suspended sediment to rivers. These signals, generated in upland erosional areas, are filtered by alluvial storage before reaching the basin outlet. We quantified this filter using a random walk model driven by sediment budget data, a power-law distributed probability density function (PDF) to determine how long sediment remains stored, and a constant downstream drift velocity during transport of 157 km/yr. For 25 km of transport, few particles are stored, and the median travel time is 0.2 yr. For 1000 km of transport, nearly all particles are stored, and the median travel time is 2.5 m.y. Both travel-time distributions are power laws. The 1000 km travel-time distribution was then used to filter sinusoidal input signals with periods of 10 yr and 104 yr. The 10 yr signal is delayed by 12.5 times its input period, damped by a factor of 380, and is output as a power law. The 104 yr signal is delayed by 0.15 times its input period, damped by a factor of 3, and the output signal retains its sinusoidal input form (but with a power-law “tail”). Delivery time scales for these two signals are controlled by storage; in-channel transport time is insignificant, and low-frequency signals are transmitted with greater fidelity than high-frequency signals. These signal modifications are essential to consider when evaluating watershed restoration schemes designed to control sediment loading, and where source-area geomorphic processes are inferred from the geologic record.