Fig. 9: Detection of isolated signal components under noisy conditions and resolution of various representations on sine packets and Gaussian atoms. | Nature Communications

Fig. 9: Detection of isolated signal components under noisy conditions and resolution of various representations on sine packets and Gaussian atoms.

From: Time-frequency super-resolution with superlets

Fig. 9

a Procedure for computing the detection score based on the fraction of values in the target window that reside above the 95th percentile of the distribution of values of the entire representation. The natural logarithm (Ln) was applied to the distributions for visualization purposes only. b Detection score for a unit amplitude sine packet of 8 cycles @ 40 Hz, as a function of the amplitude of added white noise. c Same as in b but for a unit amplitude Gaussian atom of 10 cycles @ 40 Hz. Results in b and c were computed across 25 datasets for each noise level. Each dataset consisted of 50 trials with independent noise instantiations and the target packet was inserted in only ten trials. Error bands are SEM. d Extraction of time and frequency profiles from the representation (top) and measurement of time resolution (bottom) for two sine packets. e Temporal resolution for different representations of the signal from d. f Time-frequency resolution for the signal from d. g, h, i The same as in d, e, f, respectively, but for two Gaussian atoms. Time resolution was measured as the fraction of “empty space” in the cross-section of the representation, i.e., area of the shaded region divided by the area of the green box. The green box is defined as the rectangle that spans the space between the edges of the sine packets or between the peaks of the Gaussians, while its height is given by the value of the cross-section of the representation at the sine ending points or the peaks of the Gaussians, respectively.

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