Abstract
This paper presents a dynamic systems model of a sensorimotor synchronization (SMS) task. An SMS task typically gives temporally discrete human responses to some temporally discrete stimuli. Here, a dynamic systems modeling approach is applied after converting the discrete events to regularly sampled time signals. To collect data for model parameter fitting, a previously published pilot study was expanded. Three human participants took part in an experiment: to tap a finger on a keyboard, following a metronome which changed tempo in steps. System identification was used to estimate the transfer function that represented the relationship between the stimulus and the step response signals, assuming a separate linear, time-invariant system for each tempo step. Different versions of model complexity were investigated. As a minimum, a second-order linear system with delay, two poles, and one zero was needed to model the most important features of the tempo step response by humans, while an additional third pole could give a somewhat better fit to the response data. The modeling results revealed the behavior of the system in two distinct regimes: tempo steps below and above the conscious awareness of tempo change, i.e., around 12% of the base tempo. For the tempo steps above this value, model parameters were derived as linear functions of step size for the group of three participants. The results were interpreted in the light of known facts from other fields like SMS, psychoacoustics and behavioral neuroscience.
Highlights
Sensorimotor synchronization (SMS) is defined as the coordination of rhythmic movement with an external rhythm (Repp, 2005; Repp and Su, 2013)
The results revealed an initial overshoot in the rate of the response for increasing tempo changes, as well as an undershoot for decreasing ones, generally within 4–5 taps
To overcome the problem of unknown inter-sample behavior, we will first upsample the sampled data collected at the input/output level of the human subject such that the temporal signals of pulses can be viewed as continuous-time signals in this analysis1 We will use a dynamic systems approach with a tool which, to our best knowledge, has not been applied in the study of SMS: so-called system identification, which is a standard tool in cybernetics, control theory and systems theory
Summary
Sensorimotor synchronization (SMS) is defined as the coordination of rhythmic movement (motor) with an external rhythm (sensory) (Repp, 2005; Repp and Su, 2013). We are dealing with a discrete task of generating rhythmic impulses, but we take a continuous-time approach as in dynamic systems theory The difficulty in such an approach to SMS, as reported by Michon and Van der Valk (1967), is that the discrete nature of typical tapping/clapping experiments obstructs the underlying continuous process from manifestation. To overcome the problem of unknown inter-sample behavior, we will first upsample the sampled data collected at the input/output level of the human subject such that the temporal signals of pulses can be viewed as continuous-time signals in this analysis We will use a dynamic systems approach with a tool which, to our best knowledge, has not been applied in the study of SMS: so-called system identification, which is a standard tool in cybernetics, control theory and systems theory. The raw data must be processed before being used in our systems modeling approach as described in section “Data Preperation.”
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