Adaptive Generalised Fractional Spectrogram and Its Applications
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Adaptive Generalised Fractional Spectrogram and Its Applications Peeyush Sahay1 · B. S. Teza1 · Pranav Kulkarni1 Vikram M. Gadre1
· P. Radhakrishna2 ·
Received: 19 July 2018 / Revised: 27 April 2020 / Accepted: 30 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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 transformbased 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. Keywords Higher-order chirps · Synthetic aperture radar · Short-time fractional Fourier transform · Short-time generalised time–frequency transform · Time–frequency distribution
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00034020-01442-6) contains supplementary material, which is available to authorized users.
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Peeyush Sahay [email protected]
Extended author information available on the last page of the article
Circuits, Systems, and Signal Processing
1 Introduction Non-stationary signals such as higher-order polynomial chirps are present in many practical systems like radar, sonar, and bio-medical signal processing [5,7,18,28, 31,42]. Non-stationary signals can be analysed using time–frequency analysis for classification, detection, and feature extraction purpose in many fields [8,9,38]. The short-time Fourier transform (STFT)-based spectrogram is one of the simplest ways of representing them in the time–frequency plane, but it is not suitable to localise a large variety of signals such as chirp signals. Therefore, alternative time–frequency distributions (TFDs) are proposed in the literature, such as the Wigner-Ville distribution (WVD) [42], polynomial WVD [7,42], chirplet transform-based spectrogram [42], polynomial chirplet transform-based spe
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