We present an analytical method for observation of the gravity waves (GWs) in the atmosphere from the amplitude of the radio occultation (RO) signal. We found the height dependence of the GW phase and amplitude (the GW portrait) using for example the amplitude data corresponding to one of the GPS/Meteorology (GPS/MET) RO events. We estimated the horizontal wind speed perturbations, which are in fairly good agreement with radiosonde data. The horizontal wind speed perturbations v(h) are changing in the range v ~ ¿ 1--¿9 m/s with vertical gradients dv/dh ~ ¿ 0.5--¿15 m/(s km) in the height interval 10--40 km. The height dependence of the GW vertical wavelength has been inferred through the differentiation of the GW phase. Analysis of this dependence gives the estimation of the GW intrinsic phase speed, which varies for the considered event in the interval 1.5--5 m/s. Thus the analytical method has the capability to extract important information from the amplitude of the RO signals helpful for studying the GW activity in the atmosphere.