A robust high-resolution time-frequency representation based on the local optimization of the short-time fractional Fourier transform.

The Locally Optimized Spectrogram (LOS) defines a novel method for obtaining a high-resolution time–frequency (t,f) representation based on the short-time fractional Fourier transform (STFrFT). The key novelty of the LOS is that it automatically determines the locally optimal window parameters and fractional order (angle) for all signal components, leading to a high-resolution and cross-terms free time–frequency representation. This method is suitable for multicomponent and non-stationary signals without a priori signal information. Simulated signals, real biomedical applications, and various measures are used to validate the improved performance of the LOS and compare it with other state-of-the-art methods. The robustness of the LOS is also demonstrated under different signal-to-noise ratio (SNR) conditions. Finally, the relationship between the LOS and other time–frequency distributions (TFDs) is depicted and a recursive formulation is presented and shows the trade-off between the cross-terms suppression and auto-terms resolution.