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In high-speed serial links, the data rates reach the multigigabits per second, and continue to increase. Jitter is 1 of the most important parameters used to characterize high-speed serial link performances. Generating white and colored noise synthetic jitter patterns would allow to better analyze the effect of jitter in a system for design verification. The standard organizations give separated budgets for random and deterministic jitter. Being able to model the phase noise of the different components of SerDes, generating corresponding time jitter, and decomposing it into deterministic and random jitter would help designers to better specify future SerDes systems. In our knowledge, there has been proposed no other study until today presenting a complete tutorial about jitter, its definition, its relation with phase noise, how to generate different white or colored noise patterns, and how to decompose random from deterministic jitter. This paper presents for the first time a complete study about jitter, by giving its definition, its relation with phase noise, and information on how to measure the jitter in the frequency and time domain. Furthermore, a new method for generating Gaussian distribution synthetic jitter patterns from colored noise profiles is presented. A novel technique of jitter decomposition into random and deterministic jitter is given. This technique is validated with generated and measured jitter patterns.