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Expressions are developed for the power spectral density (PSD) of a pulsed ultra wide band (UWB) signal for which the pulse repetition frequency (PRF) is directly modulated by a known time function. Parallels are drawn to the analog frequency-modulation (FM) case. An example for the swept-PRF case is provided. This work is part of a continuing effort to characterize UWB emissions, and was sponsored by the Defense Advanced Research Projects Agency (DARPA) under the NETEX program.