Time-frequency super-resolution with superlets

Abstract Due to the Heisenberg–Gabor uncertainty principle, finite oscillation transients are difficult localize simultaneously in both time and frequency. Classical estimators, like short-time Fourier transform or continuous-wavelet optimize either temporal frequency resolution, find a suboptimal tradeoff. Here, we introduce spectral estimator enabling time-frequency super-resolution, called superlet, that uses sets of wavelets with increasingly constrained bandwidth. These combined geometrically order maintain good resolution single gain upper bands. The normalization set facilitates exploration data scale-free, fractal nature, containing packets self-similar across frequencies. Superlets perform well on synthetic brain signals recorded humans rodents, resolving high bursts excellent precision. Importantly, they can reveal fast transient events trials may be hidden averaged spectrum by other methods.