Abstract
Hz). How- ever, the TF plots constructed using both the methods were almost iden- tical (Figs. 3 and 4). For quantitative analysis, we divided the TF plots into bins of time 12-ms and frequency 1.3 Hz. The absolute difference in the two dictionaries was less than 3% for more than 90% of the T-F bins. The mean absolute difference was 1.4%. Even at half the sam- pling frequency, which had the maximum bias in the dyadic case, the mean absolute difference was 1.31%. The power-frequency plot con- structed by averaging the TF plot over time differed by less than 1.37% at any time ( %). The power-time plot at any given frequency differed by, on average, less than 1%. Hence, the TF plot was essentially unaffected by the frequency bias in dyadic MP. To explain this we looked at the properties of the atoms in the biased frequencies. We observed a high concentration of small scale atoms (76.4% against 15% at unbiased frequencies) in these re- gions. Small scale values are highly localized in time but widely spread across frequency; as a result there was frequency smoothing due to small s atoms. Hence, despite the large number of atoms there was no power concentration in the biased frequencies, thus giving essentially the same results as the stochastic MP. V. C ONCLUSION
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