Superlets: time-frequency super-resolution using wavelet sets

Time-frequency analysis is ubiquitous in many fields of science. Due to the Heisenberg-Gabor uncertainty principle, a single measurement cannot estimate precisely the localization of a finite signal in both time and frequency. Classical spectral estimators, like the short-time Fourier transform (STFT) or the continuous-wavelet transform (CWT) optimize either temporal or frequency resolution, or find a tradeoff that is suboptimal in both dimensions. Following the concept of optical super-resolution, we introduce a new spectral estimation method that enables time-frequency super-resolution. Sets of wavelets with increasing bandwidth are combined geometrically in a superlet to maintain the good temporal resolution of wavelets and gain frequency resolution in the high frequency range. We show that superlets outperform the STFT and CWT on synthetic data and brain signals recorded in humans and rodents. Superlets are able to resolve temporal and frequency details with unprecedented precision, revealing transient oscillation events otherwise hidden in averaged time-frequency analyses.