Minimum-latency Time-frequency Analysis Using Asymmetric Window Functions

We study the real-time dynamics retrieval from a time series via the time-frequency (TF) analysis with the minimal latency guarantee. While different from the well-known intrinsic latency definition in the filter design, a rigorous definition of intrinsic latency for different time-frequency representations (TFR) is provided, including the short time Fourier transform (STFT), synchrosqeezing transform (SST) and reassignment method (RM). To achieve the minimal latency, a systematic method is proposed to construct an asymmetric window from a well-designed symmetric one based on the concept of minimum-phase, if the window satisfies some weak conditions. We theoretically show that the TFR determined by SST with the constructed asymmetric window does have a smaller intrinsic latency. Finally, the music onset detection problem is studied to show the strength of the proposed algorithm.