Kuc R
Ultrason Imaging. 1984 Jan;6(1):24-36. doi: 10.1177/016173468400600103.
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 insure that the filter is causal, the minimum-phase constraint 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 log-magnitude characteristic was evaluated to determine the phase of the filter. The inverse Fourier Transform of the resulting real and imaginary components of the frequency transform produces the finite-duration unit-sample 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 smaller. 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 log-magnitude characteristic is included in the Appendix.
已观察到柔软生物组织呈现出声衰减对数幅度特性，该特性随频率近似呈线性函数增加。本文描述了一种有限脉冲响应（FIR）数字滤波器模型的实现，用于在数字计算机上模拟这种行为。为确保滤波器是因果的，施加了最小相位约束。对于最小相位滤波器，对数幅度和相位特性构成希尔伯特变换对。对线性对数幅度特性的离散时间希尔伯特变换进行评估以确定滤波器的相位。频率变换所得实部和虚部的逆傅里叶变换产生数字滤波器模型的有限时长单位样本响应。使用具有随频率线性损耗特性的有机玻璃材料的实验结果表明，最小相位模型比线性相位模型更精确，导致预测时间波形与观测时间波形之间的均方根误差小3倍。讨论了改变采样周期和FIR滤波器大小的影响。附录中包含一个用于根据对数幅度特性的斜率计算最小相位单位样本响应的FORTRAN程序。
