I report here some observations from studies conducted on this comb reported by Michal in #66635.
The amplitude of the spectral lines appears to scale approximatively as f^−2.5. Figure 1 shows the ASD of 70k sec of Hrec data, 200 sec fftlength from the long lock on April 25-26, with a comparison with reference power laws: f^−2 (characteristic of a triangular wave), f^−2.5, and f^−3. This suggests that the signal may originate from a triangle wave subsequently filtered by a smoothing filter, such as a low-order low-pass filter, with a frequency response approximately f^−0.5 in the observed range. Alternatively, this could correspond to the action of a fractional integrator of order 0.5.
Another possibility is that the source is a sawtooth wave (amplitude scaling as f^−1), which passes first through an integrator (yielding another f^−1 contribution), and then through a low-pass filter, producing a total spectral fall-off of approximately f^−2.5. A square wave undergoing double integration followed by additional filtering could also yield a similar spectral profile.
From Figure 2-4, where each colored vertical line identifies a comb family, it appears to be more than one comb present at this frequency range, and that comb lines have structure.
A few observations: the comb lines have a (variable) width, equal to ~0.1 Hz at ~20 Hz, increasing with frequency. The line spacing within the 20-100 Hz range is approximately 2.9±0.1 Hz.This means that,
assuming the triangular wave model, the waveform is not strictly periodic (ideal period = 1/2.9... sec), but subject to frequency noise which causes modulation. This frequency modulation (~0.1 Hz) results in line broadening, sidebands, and shoulders. It affects all harmonics consistently, leading to overlaps, beating patterns, and generation of new frequencies via intermodulation.
These effects may explain the observed broadening, peak splitting, and emergence of intermodulation components.
I report below the measured peak frequencies in the range 20-120 Hz:
Comb starting at 20.335 Hz (main set): [20.335, 23.19, 26.04, 28.935, 31.83, 34.685, 37.6, 40.49, 43.385, 46.285, 49.185, 52.08, 54.98, 57.885, 60.78, 63.68, 66.59, 69.5, 72.385, 75.305, 78.185, 81.105, 84.015, 86.94, 89.835, 92.765, 95.67, 98.57, 101.47, 104.37, 107.275]
Comb starting at 21.305 Hz: [21.305, 24.21, 27.115, 30.02, 32.925]
Comb starting at 22.275 Hz: [22.275, 25.18, 28.085, 30.99]
Comb starting at 31.955 Hz: [31.955, 34.86, 37.77, 40.675, 43.575, 46.48, 49.39, 52.285, 55.185, 58.085, 60.98]
The spacing between the first three sets of combs is ~0.97 Hz. The fourth set is spaced ~0.12 Hz from the first set.
It remains to be investigated whether further analysis of these values will shed more light on the nature of the signal underlying the observed comb structure in Hrec.
