差分谱驱动的STFT窗长自适应优化方法
Differential Spectral-Driven Adaptive STFT Window Length Optimization
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摘要: 在许多领域中,对频谱测量精度的要求很高。短时傅里叶变换(Short-Time Fourier Transform, STFT)因结构简单、计算高效,成为最基础的时频分析工具之一。然而,STFT采用固定窗长,在处理非平稳信号时难以同时兼顾时间分辨率和频率分辨率,会影响频谱测量的精度。针对此问题,本文提出一种基于差分谱特征的自适应窗长调整策略(Differential spectral-driven adaptive STFT, DSD-ASTFT),用于优化时频表示(Time-Frequency Representation, TFR)的质量。该方法通过计算相邻时刻幅值谱的归一化差值谱,构建一个局部动态频率变化率评估指标,并依据该指标调整后续快速傅里叶变换(Fast Fourier Transform, FFT)的窗长参数,在频率快速变化处采用短窗以提升时间分辨率,在相对平稳段采用长窗以改善频率分辨率。最终,组合多帧FFT得到的频谱生成高质量TFR。实验结果表明,所提算法的计算复杂度接近STFT,频谱测量精度有所提高,在信噪比大于15 dB时,正弦型线性扫频信号瞬时频率的归一化均方误差趋于稳定,相较于文中所提其余ASTFT算法降低了5 dB以上。这一成果展示了其在实时ASTFT方案设计方面的潜力和可行性,并为进一步研究如何更高效、精确地分析具有复杂时频特征的非平稳信号奠定了坚实的基础。此外,该方法的有效性验证了在特定应用背景下,通过合理平衡计算效率与时频分辨率来提升信号处理性能的可能性。需指出,DSD-ASTFT方法的有效性依赖于信号局部可近似为线性调频模型这一前提,其卓越性能主要体现在处理时频结构连续变化的非平稳信号,对于频谱结构稳定或发生突变的信号,此方法的窗长调整机制可能无法被有效触发。Abstract: 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.
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