Abstract: With excellent time-frequency combination, S transform has been extensively used in the field of signal processing. 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 different algorithms, but the related references about it cannot be found. The frequency-domain algorithm of discrete S transform 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 distribution 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.

Key words: time-frequency analysis, discrete S transform, time-domain algorithm, frequency-domain algorithm, periodicity

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。

关键词: 时-频分析, 离散S变换, 时域算法, 频域算法, 周期性