An Empirical Investigation Into the Time and Frequency Response Characteristics of Hopf Resonators

Abstract

We present an empirical investigation of software developed by the Science and Music Research Group at the University of Glasgow. Initially created for musicological applications, it is equally applicable in any area where precise time and frequency information is required from a signal, without encountering the problems associated with the uncertainty principle. By constructing a bank of non-linear tuned resonators (`detectors'), each of which operates at a Hopf bifurcation, it is possible to detect frequencies within half a period of oscillation, even in the presence of wideband noise. The time and frequency response characteristics of these detectors will be examined here.