Time-Frequency Analysis Based on Constant-Q Transform With Nonstationary Gabor Frames

The low-frequency line spectrum of ship-radiated noise exhibits characteristics of high intensity and excellent stability, making it highly significant for detecting low-noise underwater targets. Short-time Fourier transform (STFT), a traditional method used for line spectrum detection, maintains a fixed time-frequency resolution, which proves inadequate in accommodating the characteristic non-uniform energy distribution pattern of ship-radiated noise. To attain flexible resolution analysis, this paper employs constant-Q transform with nonstationary Gabor frames (CQ-NSGT) for time-frequency analysis, which has been extensively applied in the field of music signal processing. The method comprises three critical steps: First, the time-frequency grid is partitioned to ensure a constant-Q factor. Second, Gabor frame atoms are constructed by translating and scaling the window function along the time-frequency grid. Finally, Gabor frame coefficients and power are computed. Four different window functions were used in this paper to implement CQ-NSGT. The results indicate that the Blackman-Harris window yields the best performance. Results of experimental data processing reveal that CQ-NSGT requires considerably less processing time and achieves higher frequency resolution at the low-frequency part compared to the traditional constant-Q transform (CQT) and STFT. Moreover, CQ-NSGT exhibits a higher signal-to-noise (SNR) ratio at the line spectra. This approach offers a robust and computationally efficient solution for time-frequency feature extraction of underwater radiated noise, enabling effective target detection and recognition.