The analysis of the Doppler echo in the general case involves a number of variables that tend to obscure a physical interpretation of our final results. We ll thus begin by analyzing a simplified case and interpret the results obtained before considering the general case. For this, we ll begin by analyzing the case in which the antenna is directed along the flight path and the antenna pattern is thin; that is, its width in the azimuth direction is very narrow. This simplification eliminates the azimuth coordinate in our analysis and so eliminates a number of parameters involved in our analysis, such as the effect of the antenna pattern width in a direction perpendicular to the flight path and pointing the antenna in a direction off the flight path. The thin antenna case thus will enable us to obtain analytic approximations from which a physical interpretation of the contribution of the various parameters to the Doppler spectrum can be obtained. This understanding will assist us in the interpretation of the expressions we ll obtain for the general case in which the expressions are involved and require a computer for their evaluation.