Abstract: Digital synthesizers of frequency are used extensively in most technological domains as the instrumentation, the communication and the modern telecommunications systems. In this study, one proposes to present some techniques of frequency synthesis in these two analog and digital forms. The three basic synthesis techniques are namely direct analog synthesis, direct digital synthesis and indirect analog synthesis. For the case of frequency indirect synthesis, we have used the technique of Phase Locked Loop PLL in frequency synthesizers design such as, for example, fractional-N PLL synthesizers and sigma-delta fractional-N PLL`s synthesizers. We have also proposed and studied a digital frequency synthesizer functioning as a digital oscillator to controlled amplitude and frequency. The conceived synthesizer was built from the discretization of sine function. The gotten algorithm has been implemented on the SHARC EZ-KIT Lite, based around the ADSP-21065L Digital Signal Processor DSP. The algorithm has been applied to the amplitude modulation and the frequency. The satisfactory results of implementation have been presented and discussed in various cases in the goal to validate the analytic study features.