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A new mathematical analysis to predict the magnitude size of the distortion products from the signal up-conversion process output is presented. The signal up-conversion process converts the digital baseband from the analog baseband into a radio frequency signal. When the signal baseband involves frequency offsetting then occurring a number of distortion products which can reduce the dynamic range so it is difficult to meet the spectrum mask requirements within the operating band. This paper will focus on methods of new mathematical analysis using a continuous frequency range and only applies to a single side band tone, with constant amplitude into any value of frequency offsets. The novel contribution to the analysis starts at generating the gate signal and convolution of the gate signal into the reference carrier signal. The results show very close between the simulation results and the calculation of the predicted location of the distortions