Table 1
List of simulations performed. 1st col.: Simulation number; 2nd col.: Brief signal description; 3rd col.: Total signal duration; 4th col.: Fundamental frequency; 5th col.: Composition of each complex tone (number of harmonic and its amplitude, n/a for IRN); 6th col.: Amount of mistuning of all components (simulation II only); 7th col.: Number if iterations of the IRN (simulation V only); 8th col.: Gain of additive Ν(0, 1)-distributed Gaussian noise; 9th col.: Signal-to-Noise Ratio computed across the whole signal duration (n/a for IRN); 10th col.: Initial PM-HLL oscillator frequency: 11th col.: Tracking error in terms of mean and standard deviation across the whole signal duration, excluding the time period of initial convergence (cf. Sect. 3).
| Signal | T/ms | f0/Hz | # of harmonic (amplitude) | fd/Hz | # | Noise gain | SNR/dB | Initial osc. freq. fc,0/Hz | Tracking error mean (std)/Hz | |
|---|---|---|---|---|---|---|---|---|---|---|
| I | Complex tone with fixed fundamental frequency | 400 | 98.5 (1st half) | #1 (0.5), #3 (0.9), #4 (0.7), #6 (0.9), #7 (0.7) | 0 | – | 0.1, 0.5, 1.0 | 21.5, 7.5, 1.5 | 99.5 | 0.01 (0.37), 0.02 (0.59), 0.12 (0.81) |
| 101.0 (2nd half) | ||||||||||
| II | Complex tone with fixed fundamental frequency | 400 | 98.5 (1st half) | #1 (0.5), #3 (0.9), #4 (0.7), #6 (0.9), #7 (0.7) | +6, −6 | – | 0.5 | 7.5 | 99.5 | +1.21 (0.59), −1.39 (0.71) |
| 101.0 (2nd half) | ||||||||||
| III | Complex tone with fixed fundamental frequency and missing fundamental | 400 | 98.5 (1st half) | #6 (0.9), #7 (0.7) | 0 | – | 0.5 | 4.1 | 99.5 | 0.03 (0.56) |
| 101.0 (2nd half) | ||||||||||
| IV | Complex tone with linear sweep of its fundamental | 100 | 96.0 (start) | #1 (0.5), #3 (0.9), #4 (0.7), #6 (0.9), #7 (0.7) | 0 | – | 0.1, 0.5, 1.0 | 21.3, 7.6, 1.4 | 99.5 | 0.45 (0.26), 0.44 (0.50), 0.90 (0.50) |
| 103.0 (end) | ||||||||||
| V | Iterated rippled noise (IRN) | 200 | 98.0 | – | – | 5, 3, 1 | – | – | 99.5 | 0.00 (0.51), 0.15 (0.55), 0.60 (0.58) |
| VI | Major chord with three tones (in semitones: 1st, 4th and 7th) at equal level | 200 | 170.0 (tone 1), 214.2 (tone 2), 254.7 (tone 3) | For each tone: #3 (0.9), #4 (0.7), #6 (0.9), #7 (0.7) | 0 | – | 1.5 | −2.2 (one tone) | 183.6 (tone 1), 231.3 (tone 2), 275.1 (tone 3) | −0.7 (1.6), −1.0 (3.6), −0.5 (2.7) |
| +3.1 (three tones) |
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