The Analytic Signal Magnitude for Improved Ultrasonic Signatures

Conventional pulse-echo ultrasonic receivers rectify the received signal. Because the signature of the reflecting interfaces is modulated by the predominant ultrasonic frequency, interpretation of this signal in terms of the structure of the reflecting interfaces is difficult. Smoothing, as by an R-C filter, ameliorates this effect, giving a less confusing display at the expense of resolution. The magnitude of the analytic signal, on the other hand, represents the shape of the energy packets arriving from the reflecting interfaces. Since this signature is free of modulation effects, interpretation of the signal in terms of the reflecting interfaces is more straightforward. Furthermore, smoothing is not normally needed. The analytic signal magnitude can be obtained by several means. The implementation used in this study is particularly suited for digital data processing. The Hilbert Transform of the received signal (the "real part") is obtained with the aid of the Fast Fourier Transform. This produces the quadrature component (the "imaginary part"). The magnitude is calculated from both these components. In contrast to signal processing techniques involving deconvolution, this technique is surprisingly robust with respect to noise and quantization. Typical signatures obtained with this technique are demonstrated.