A systematic investigation of codas in media with Gaussian and exponential correlation function is presented. By means of various tools such as the wavelet decomposition, it is shown that the spectral analysis of codas has to be limited to a restricted time interval whose boundaries are given. When this condition is fulfilled and when the fluctuations of the sound velocity are smaller than 4%, the average codas power spectrum is indeed proportional to the backscattering coefficient as predicted by the linear theory developed by Aki and Chouet. This coefficient can be successfully inverted to retrieve the statistical properties of the velocity distribution. Various numerical and practical recommendations are suggested. ¿American Geophysical Union 1991