A generic parametric model for ultrasonic signal analysis

Parametric echo modeling and estimation approach has been widely used in recent years for ultrasonic echo analysis and assessment of NDE test parameters. Parametric models such as Gaussian echo, Gaussian Chirplet have been utilized in the context of model-based echo estimation and sparse signal decomposition. These models are mathematically tractable, convenient for numerical calculations, and have explicit Time-Frequency representations. As a result they have been used extensively in acoustic signal processing. However, most often these models are not as flexible to represent complex shape ultrasonic echoes. A generic echo model that can be optimized to represent complex shape echoes is highly desirable, for example, for modeling frequency dependent attenuation and dispersion effects in a propagation path, deconvolution of reflector echoes in presence of pulse variance. In this study, we propose a generic echo model to characterize complex shape ultrasonic echoes. This echo model is inspired from the analytic signal representation in which an ultrasonic echo is contemplated in terms of an envelope and sinusoidal components. The echo envelope is modeled as a sum of a number of fixed-width Gaussian Functions (GFs) whereas the echo sinusoidal is modeled as a linear chirp signal. The number and bandwidth of GFs are set based upon the spectral characteristics of the transducer impulse response. This Gaussian mixture representation accounts for skewed shape envelopes while the linear chirp accounts for small frequency drifts in the sinusoidal. An optimization algorithm is developed to estimate the generic model parameters. The performance of parameter estimation is verified using pulse-echo wavelets acquired from several different transducers and measurement conditions. Finally, this echo model is incorporated into a superimposed echoes estimation algorithm. Estimation results clearly demonstrate the advantage of this model compared to the existing alternatives. The potential applications of this type of model are numerous: ultrasonic deconvolution in presence of pulse variance, resolution of complex overlapping pulses, and NDE parameter estimation.