Differential Spectral-Driven Adaptive STFT Window Length Optimization

There is a high demand for spectrum measurement accuracy in many fields. The short-time Fourier transform （STFT）， possessing a simple structure and computational efficiency， serves as one of the most fundamental time-frequency analysis tools. However， it employs a fixed window length when processing nonstationary signals， making it difficult to achieve an optimal trade-off between time and frequency resolution， which compromises the accuracy of the spectrum measurements. To address this issue， this study proposes an adaptive window length adjustment strategy based on differential spectrum features to optimize the quality of time-frequency representation （TFR）. This method calculates the normalized differential spectrum of the amplitude spectra between adjacent time segments to construct a local dynamic frequency variation rate evaluation metric. Based on this metric， the window length parameter for subsequent fast Fourier transform （FFT） operations is adaptively adjusted. Shorter windows are used in regions of rapid frequency variation to enhance the time resolution， whereas longer windows are applied in relatively stationary segments to improve the frequency resolution. Finally， a high-quality TFR is generated by integrating the spectral information obtained from multiple FFT frames. The experimental results showed that the computational complexity of the algorithm was comparable to that of the STFT. Moreover， this method significantly enhances measurement accuracy. Experimental results demonstrate that the computational complexity of the proposed algorithm is comparable to that of the STFT， while the spectral estimation accuracy is improved. When the signal-to-noise ratio exceeds 15 dB， the normalized mean square error of the instantaneous frequency estimation for sinusoidal linear sweep signals stabilizes， which is reduced by more than 5 dB compared to other ASTFT algorithms discussed in the paper. This achievement demonstrates the potential and feasibility of the proposed method for real-time adaptive STFT （ASTFT） applications and lays a solid foundation for further research on more efficient and accurate analysis of nonstationary signals with complex time-frequency characteristics. Additionally， the effectiveness of this method validates the possibility of enhancing signal processing performance by reasonably balancing computational efficiency and time-frequency resolution in specific application contexts. The effectiveness of the differential spectral-driven adaptive STFT （DSD-ASTFT） method relies on the assumption that the signal can be approximated locally as a linear frequency-modulated model. Its superior performance is particularly evident in processing nonstationary signals with continuously varying time-frequency structures； however， for signals with stable spectral structures or abrupt changes， the window-length adjustment mechanism of this method may not be triggered effectively.