Pulse compression in a time variant system with application to ultrasonic vibrometry

Abstract

Pulse compression is normally applied only to time-invariant systems, as the variation of a system's properties during its interrogation violates assumptions of the compression process. However, there is an exact solution to the pulse-compression problem when the time variance satisfies two criteria, which are the same as those required for the operation of an ultrasonic vibrometer in the context of a tissue elastography system. One is that the variations be very small in comparison with the wavelength of the interrogating ultrasound. The other is that the bandwidth of the variations be within one Nyquist band as sampled by the periodic interrogation signal. The solution to this problem involves a step-wise interpolation of the static pulse-compression transfer function in the frequency domain. This technique, in conjunction with the selection of an appropriate interrogation signal, offers significant advantages in measurement time or measurement resolution for an ultrasonic vibrometer limited by additive noise at the receiver. The characteristics of optimal interrogation signals for this technique are the signal's crest factor, spectral energy distribution, and phasing. These relate to the intended compression pulse, the noise, and the static response of the system. The technique has been demonstrated analytically, experimentally, and with numerical models.