Modeling acoustic attenuation of soft tissue with a minimum-phase filter

Soft biological tissue has been observed to exhibit an acoustic attenuation log-magnitude characteristic which increases as an approximately linear function of frequency. This paper describes the implementation of a finite-impulse-response (FIR) digital filter model for simulating this behavior on a digital computer. To inaure that the filter is causal, the minimum-phase conatraint is imposed. For minimum-phase filters, the log-magnitude and phase characteristics form a Hilbert Transform pair. The discrete-time Hilbert Transform of the linear logmagnitude characteristic was evaluated to determine the phase of the filter. The inverse Fonrier Transform of the resulting real and imaginary components of the frequency transform produces the finite-duration unitsample response of the digital filter model. Experimental results using plexiglas material, which has a linear-with-frequency loss characteristic, indicate that the minimum-phase model is more accurate than the linear-phase model, resulting in a rms error between predicted and observed time waveforms that is 3 times maller. The effects of varying the sampling period and the size of the FIR filter are discussed. A FORTRAN program to calculate the minimum-phase unit-sample response from the slope of the logmagnitude characteristic is included in the Appendix.