Clock signal generation circuitry includes input circuitry for receiving a frequency control input signal and a clock signal and generating a memory address therefrom, a memory for storing digital data indexed by the memory address and representing real and imaginary parts of a complex digital waveform, and digital to analog conversion circuitry. The digital to analog conversion circuitry includes real-part digital to analog conversion circuitry for converting digital data retrieved from the memory and representing the real part of the complex waveform into a real-part analog signal and imaginary-part digital to analog conversion circuitry for converting digital data retrieved from the memory and representing the imaginary part of the complex waveform into an imaginary-part analog signal. The clock signal generation circuitry also includes analog filtering circuitry having real-part filtering circuitry for filtering the real-part analog signal to generate a filtered real-part analog signal and imaginary-part filtering circuitry for filtering the imaginary-part analog signal to generate a filtered imaginary-part analog signal. Analog to digital conversion circuitry is provided for converting the filtered real-part and imaginary-part analog signals into a digital clock signal at a rate near an integer multiple of a frequency of the filtered real-part and imaginary-part analog signals.