Frequency-varying group delay estimation using frequency domain polynomial chirplet transform

• We develop group delay rotating operator and group delay shifting operator.
• We develop frequency domain polynomial chirplet transform (FPCT).
• We develop PCTF based frequency-varying group delay estimation method.
• The FPCT outperforms STFT, wavelet transform and Wigner–Ville distribution.
• We apply the FPCT on experimental Lamb wave signal to estimate velocity dispersive curve.

In signal processing, group delay (GD) is used to measure the time delay of a signal passing through a system. It is an important parameter to be estimated for identifying, localizing, and tracking radiating sources. Moreover, it is conducive to acquire the characteristics and predict the response of the system. The GD is calculated by differentiating, with respect to frequency, the phase response versus frequency of the device under test, i.e., the slope of the phase response at any given frequency. In a linear phase system, the GD is constant. In practice, the GD of a signal passing through the system under test could vary with frequencies. Most GD estimation techniques are designed to estimate the constant GD instead of the frequency-varying GD. Time–frequency analysis is a potential tool for frequency-varying GD estimation. In this paper, a frequency domain polynomial chirplet transform (FPCT) is proposed. It first applies a GD-rotating operator and GD-shifting operator on the spectrum of the signal successively. Then, the inverse Fourier transform is performed on every windowed spectrum that is obtained by sliding the window throughout the shifted spectrum of the signal. An advantage of the FPCT is that it can obtain well-concentrated time–frequency representation so as to estimate nonlinear GD for wideband signals. The comparisons between the FPCT and other time–frequency analysis methods are provided to verify the performance of the FPCT in estimating the nonlinear GD. In addition, the study on experimental Lamb wave signal validates the effectiveness and potential of the FPCT.