Abstract: A “frequency shifter” is a clock synthesis system, that includes either a multiplexer or a multi-modulus divider (MMD), a fractional frequency divider, a tunable delay element, a sawtooth signal generator, in addition to other synchronization and control circuits. The generated sawtooth signal is used to control the delay of the tunable delay element, which in turn is used to adjust the phase of the signal generated by either M-to-1 multiplexer or the MMD, reducing its timing errors, and improving the spectral purity of the generated clock signal.