Design and analysis of non-uniform rate digital controllers

Various applications in digital systems require the involvement of concepts from signal processing and filtering. These specific problems often need the linear dynamic systems to have a transfer function that can specify the behavioural characteristics of the system. When operating in the digital domain, such functions can effectively be used to approximate the same characteristics over the frequency range of importance as any given continuous-time transfer function. In the case with uniform sampling, linear systems theory can directly provide an answer to determine the frequency response. However, when the element of randomness is added to the sample rate of the discrete controller, the common analysis technique of substituting z=e^jw will not give the correct result. This paper therefore places an emphasis on the Fourier analysis and highlights a technique to compute the magnitude and phase of a non-uniform rate transfer function at various frequencies in the time domain.