When STFT Meets Quadratic Frequency Modulation Signal

Short time Fourier transform (STFT) is an excellent two-dimensional time-frequency analysis tool that can effectively analyze the time-frequency characteristics of signals. However, it is difficult for STFT to deal with complex non-stationary signal such as quadratic frequency modulation (QFM) signal. This paper proposes two types of short-time quadratic frequency modulation fractional Fourier transform (QFMFRFT), windowed form and convolutional form, based on QFMFRFT and STFT. These two transforms are derived from two equivalent forms of STFT. Corresponding to physical explanations of the STFT, the physical explanations of the proposed transforms are discussed and compared. Specifically, the definitions, inverse transformations, properties, computational complexity and window function selection of the two transforms are introduced respectively. Moreover, the advantages and applications of the two methods are discussed. Under strong noise conditions (-15 dB Signal-to-Noise Ratio), the proposed methods maintain clear component separability for multi-component QFM signals where conventional methods fail to distinguish components. Simulations results demonstrate the obvious advantages of the proposed methods over traditional methods on inverse synthetic aperture radar imaging and parameter estimation.