离散S变换的频域算法和时域算法比较

摘要

在信号处理领域，S变换具有良好的时频结合特性，应用广泛。在实际系统中，S变换通过离散数值方法实现，有频域和时域两种形式，文献中多使用频域形式。在用S变换对一些信号作时-频分析时，频域和时域两种实现形式得到的时-频谱图有明显的差异，但没有文献对此问题进行相关讨论。离散S变换的频域算法使用快速Fourier变换（FFT）和其逆变换（IFFT）实现，但由于Fourier变换蕴含周期特性，一些信号的S变换时-频谱图在始末两端会出现虚假频率信息，干扰信号的时-频分析结果。在研究S变换理论的基础上，给出离散S变换的时域实现。离散S变换的时域算法克服了频域算法的缺点，能更准确反映信号的时-频分布情况。通过对比实验，验证了时域算法的有效性。将S变换的离散时域算法用于地震数据拓频处理，结果显示方法能有效增强信号分辨率。%With excellent time-frequency combination, S transform has been extensively used in the field of signal pro-cessing. In physical system, S transform can be finished with discrete numerical calculation, providing a correct basis for analyzing and solving problems. The discrete S transform can be implemented in two ways which are frequency-domain and time-domain and the former being used widely. There are some obvious differences on signal spectrograms by differ-ent algorithms, but the related references about it cannot be found. The frequency-domain algorithm of discrete S trans-form is usually implemented by FFT and IFFT. Due to the inherent periodicity of Fourier transform, the ends of signal spectrogram generated by frequency-domain algorithm have false frequency information, interfering signal time-frequency analysis. Based on the study of basic principles of S transform, this paper proposes a time-domain algorithm of discrete S transform, which overcomes the shortages of the frequency-domain algorithm and can map signal time-frequency distribu-tion more accurately. The paper validates the algorithm of time-domain by introducing comparative tests, and gives using recommendations. The frequency-broadening processing of the algorithm is used real seismic data, and the result indicates that this method can availably improve seismic signal resolution both in time and frequency domain.