Singular superlet transform achieves markedly improved time-frequency super-resolution for separating complex neural signals

Time-frequency decomposition is a well-established method to unmix signals generated by multiple sources with unique characteristics. However, there are cases of high signal complexity where existing time-frequency decomposition tools are insufficient for localizing and representing short-bursting signals. One example is the currently highly popular extracellular low-impedance recordings from multi-electrode arrays in the brain in vivo where each neuron repeatedly generates a specific signal fingerprint (characteristic spike waveform) that can be mixed with the signals of 100s of other sources, including the spikes of nearby neurons. Here we derive the singular superlet transform (SST) method, which enables highly localized representations of fast and short bursts compared to other super-resolution spectral estimators, while also requiring orders of magnitude fewer operations. We demonstrate a substantial edge of SST over current methods in isolating specific neuronal spikes with high-fidelity in challenging, complex recording signals from neocortex in vivo. We also exemplify SSTs generic signal processing capability by achieving outstanding resolution in the decomposition of complex acoustic data.