Extended variances and autoregressive/moving average algorithm for the measurement and synthesis of oscillator phase noise

Two related aspects are discussed of the recent research work carried out at Portsmouth Polytechnic in the UK regarding numerical and digital techniques for the measurement and synthesis of phase noise in oscillators. The first aspect concerns the introduction of a statistical quantity termed extended Hadamard variance to be applied in frequency stability analysis by making use of digital frequency counter measurements. The properties, the potential interest and the usefulness of this parameter are briefly demonstrated and applied to the study of a signal from a synthesizer that is frequency-modulated by white noise followed by the frequency counter and signal processing. It is shown that not only the Hadamard variance but also the Allan variance and the extended two-sample variance are sets of this variance. The second aspect refers to modern requirements for numerical simulation of random noise, emulating phase or frequency fluctuations. The authors describe the autoregressive integrated moving average technique used to generate various types of random noise, including radio propagation FM noise, and the Monte Carlo approach to transform from one distribution to another