Adaptive Generalised Fractional Spectrogram and Its Applications

Abstract

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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Acknowledgements

The authors would like to thank the DRDO, Ministry of Defence, Govt. of India for sponsorship of Peeyush Sahay, Sc ‘E’ (Ph.D. student), and B. S. Teza, Sc ‘C’ (Master student) under the R&D scheme, at IIT Bombay. The authors would like to thank Mr. Shubham Anand Jain (B.Tech, IIT Bombay), Mr. Ameya Anjarlekar (B.Tech, IIT Bombay), Mr. Adway Girish (B.Tech, IIT Bombay), Mr. Shubham Kar (B.Tech, IIT Bombay), Mr. Ayush Agarwal (B.Tech, IIT Dharwad), Mr. Shaan Ul Haque (B.Tech, IIT Bombay), Mr. Izaz Ahamed Shaik Rasheed (M.Tech, IIT Bombay), and Mr. Gaurav Pooniwala (B.Tech, IIT Bombay) for improving the quality of the paper. The authors wish to thank Curtis Condon, Ken White and Al Feng of the Beckman Institute of the University of Illinois for the bat data and for permission to use it in this paper.

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Sahay, P., Teza, B.S., Kulkarni, P. et al. Adaptive Generalised Fractional Spectrogram and Its Applications. Circuits Syst Signal Process 39, 5982–6033 (2020). https://doi.org/10.1007/s00034-020-01442-6

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Keywords

  • Higher-order chirps
  • Synthetic aperture radar
  • Short-time fractional Fourier transform
  • Short-time generalised time–frequency transform
  • Time–frequency distribution