The present paper analyses the bullwhip problem generated by exponential smoothing algorithms in both stand alone passing-on-orders mode, and within inventory controlled feedback systems. Results are predicted from transfer function analysis, and then confirmed by simulation via the Bullwhip Explorer supply chain software. A novel feature of the paper is the introduction of the matched filter concept into the exponential smoothing algorithm. This adjusts the value of the smoothing constant depending on whether the Constant, Linear, or Quadratic forecasting model is used. It is shown that matching the filter via noise bandwidth equalises the output variance when the demand is a random signal. Hence some of the unwanted effects of using the Linear and Quadratic forecasting models are attenuated. However, there is little benefit obtained by using sophisticated forecasting methods within inventory controlled feedback systems as their tracking ability is reduced.