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

TL;DR

This paper empirically investigates Hopf resonators' time and frequency response characteristics, demonstrating their ability to detect frequencies rapidly and accurately in noisy signals, with applications in musicology and signal processing.

Contribution

It provides an empirical analysis of Hopf resonators' response characteristics, highlighting their effectiveness in precise time-frequency detection in noisy environments.

Findings

Detect frequencies within half a period of oscillation

Operate effectively in wideband noise

Applicable in musicology and signal analysis

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.