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An extension of the Rowe-Prabhu method is presented for finding the power spectral density (PSD) of continuous phase modulated (CPM) signals with correlated data symbols. Correlation between symbols in different time slots is introduced by an encoder which is represented as a finite-state sequential machine. This structure simplifies any procedure for the spectral analysis of modulated signals with correlated data symbols, including the Rowe-Prabhu method. For instance, it allows a sequential computation of some of the matrices needed for this spectral analysis technique. The PSD is expressed in a compact, Hermitian matrix form that is suitable for numerical computation by a digital computer. Examples for convolutionally encoded CPM are given for the purposes of illustration, as treating such signals was the primary motivation in developing the spectral analysis algorithm that is presented in the paper.