The generalised time–frequency transform (GTFT) is a powerful tool to analyse a large variety of frequency-modulated signals. However, it is not adequate to represent the variation of frequency over time for non-stationary signals. To solve this problem, short-time GTFT and short-time GTFT-based adaptive generalised fractional spectrogram (AGFS) are proposed. The AGFS is capable of providing a high concentration, high resolution, cross-term-free time–frequency distribution for analysing multicomponent frequency-modulated signals. It is also a generalisation of the short-time Fourier transform-based spectrogram and the short-time fractional Fourier transform-based spectrogram. The uncertainty principle for short-time GTFT is derived, and its time-bandwidth product is compared with other time–frequency distributions. With the help of simulated data examples, the effectiveness of AGFS is demonstrated in comparison with other time–frequency distributions for resolving and extracting individual components of multicomponent quadratic chirps. Robustness of AGFS is demonstrated under different input signal-to-noise ratio conditions. A local spectrogram optimisation technique is adopted for AGFS to represent simulated and real chirp signals. Finally, an application of the AGFS is presented to resolve multiple ground moving targets in synthetic aperture radar data and obtain its focused synthetic aperture radar image.

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自适应广义分数谱图及其应用

广义时频变换 (GTFT) 是分析各种调频信号的强大工具。然而，对于非平稳信号来说，表示频率随时间的变化是不够的。为了解决这个问题，提出了短时 GTFT 和基于短时 GTFT 的自适应广义分数谱图 (AGFS)。AGFS 能够提供高浓度、高分辨率、无交叉项的时频分布，用于分析多分量调频信号。它也是基于短时傅里叶变换的频谱图和基于短时分数傅里叶变换的频谱图的推广。推导了短时 GTFT 的不确定性原理，并将其时间带宽积与其他时频分布进行了比较。在模拟数据示例的帮助下，与其他时频分布相比，AGFS 在解析和提取多分量二次线性调频的各个分量方面的有效性得到了证明。在不同的输入信噪比条件下证明了 AGFS 的稳健性。AGFS 采用局部频谱图优化技术来表示模拟和真实 chirp 信号。最后，提出了AGFS在合成孔径雷达数据中解析多个地面运动目标并获得其聚焦合成孔径雷达图像的应用。在不同的输入信噪比条件下证明了 AGFS 的稳健性。AGFS 采用局部频谱图优化技术来表示模拟和真实 chirp 信号。最后，提出了AGFS在合成孔径雷达数据中解析多个地面运动目标并获得其聚焦合成孔径雷达图像的应用。在不同的输入信噪比条件下证明了 AGFS 的稳健性。AGFS 采用局部频谱图优化技术来表示模拟和真实 chirp 信号。最后，提出了AGFS在合成孔径雷达数据中解析多个地面运动目标并获得其聚焦合成孔径雷达图像的应用。