njit-etd2003-081 - New Jersey Institute of Technology

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having the same mean occurrence rate .10 for the period of data collection (typically 6
minutes). The algorithm that the computer used to set the timing of the beeps was as
follows [44]. A Gaussian white-noise (GWN) signal was obtained by constructing a
sequence of Gaussian-distributed random numbers. To confine the GWN signal energy
to the spectral band of interest, the signal was digitally processed with a low-pass filter
in which the corner frequency was typically set to 0.7 Hz. The resulting band-limited
GWN signal f(t) represented the desired instantaneous pulse frequency and its reciprocal
1/f (t) the instantaneous inter-pulse interval. An internal clock kept track of the time T
that elapsed since the last pulse produced. Whenever T exceeded 1/f (t), a new pulse was
produced and T was reset to zero. Stylized representations of the band-limited GWN
signal, its theoretical power spectrum and probability distribution, and the corresponding
GWN frequency-modulated (GWNFM) pulse train are shown in Fig. 4.1. Importantly,
the mean f mean and variance σf of the (GWN) modulator signal were specified for each
6-min experimental run.
Figure 4.1 Theoretical power spectrum, time series, and probability distribution of
band-limited Gaussian white noise and corresponding frequency-modulated pulse train.