he adaptive chirplet transform and its application in GPR target detection

GPR has become an important geophysical method in UXO and landmine detection, for it can detect both metal and non-metallic targets. However, it is difficult to remove the strong clutters from surface-layer reflection and soil due to the low signal to noise ratio of GPR data. In this paper, we use the adaptive chirplet transform to reject these clutters based on their character and then pick up the signal from the UXO by the transform based on the Radon-Wigner distribution. The results from the processing show that the clutter can be rejected effectively and the target response can be measured with high SNR.

Roll angular rate extraction based on modified spline-kernelled chirplet transform

The roll angular rate is much crucial for the guidance and control of the projectile.Yet the high-speed rotation of the projectile brings severe challenges to the direct measurement of the roll angular rate.Nevertheless,the radial magnetometer signal is modulated by the high-speed rotation,thus the roll angular rate can be achieved by extracting the instantaneous frequency of the radial magnetometer signal.The objective of this study is to find out a precise instantaneous frequency extraction method to obtain an accurate roll angular rate.To reach this goal,a modified spline-kernelled chirplet transform(MSCT)algorithm is proposed in this paper.Due to the nonlinear frequency modulation characteristics of the radial magnetometer signal,the existing time-frequency analysis methods in literature cannot obtain an excellent energy concentration in the time-frequency plane,thereby leading to a terrible instantaneous frequency extraction accuracy.However,the MSCT can overcome the problem of bad energy concentration by replacing the short-time Fourier transform operator with the Chirp Z-transform operator based on the original spline-kernelled chirplet transform.The introduction of Chirp Z-transform can improve the construction accuracy of the transform kernel.Since the construction accuracy of the transform kernel determines the concentration of time-frequency distribution,the MSCT can obtain a more precise instantaneous frequency.The performance of the MSCT was evaluated by a series of numerical simulations,high-speed turntable experiments,and real flight tests.The evaluation results show that the MSCT has an excellent ability to process the nonlinear frequency modulation signal,and can accurately extract the roll angular rate for the high spinning projectiles.

Modeling and parameter identification of linear time-varying systems based on adaptive chirplet transform under random excitation

In this paper,a time–frequency algorithm based on adaptive chirplet transform for parameter modeling and identification of Linear Time-Varying(LTV)systems under random excitation is presented.It is assumed that the solution of responses of LTV structures is expressed as the sum of multicomponent Linear Frequency Modulated(LFM)signals in a short-time.Then the measured acceleration response is used to perform the adaptive chirplet transform,in which an integral algorithm is employed to reconstruct the velocity and displacement responses.The vibration differential equation with time-varying coefficients is transformed into a simple linear equation.Furthermore,for systems under random excitation,the input–output relation based on correlation function is also derived to estimate the parameters including physicals parameters and instantaneous modal parameters.The full procedure of the method is presented and validated by using simulated responses.The results show that the presented method is accurate and robust for various LTV systems under random excitation.

Subspaces of FM^mlet transform

The subspaces of FMmlet transform are investigated. It is shown that some of the existing transforms like the Fourier transform, short-time Fourier transform, Gabor transform, wavelet transform, chirplet transform, the mean of signal, and the FM-1let transform, and the butterfly subspace are all special cases of FMmlet transform. Therefore the FMmlet transform is more flexible for delineating both the linear and nonlinear time-varying structures of a signal.

Properties and convergence analysis of FM^mlet transform

The linearity,time shifting,time scaling,and time inversion properties of FMmlet transform are proved,and the frequency shifting property of one of the subspaces of FMmlet transform,namely the chirplet transform is presented.Moreover,it is proved that in the process of FMm let based atomic signal decomposition,the residual signals decay exponentially.