Kuc R, Haghkerdar K, O'Donnell M
Ultrason Imaging. 1986 Jul;8(3):196-212. doi: 10.1177/016173468600800304.
A peak in the power cepstrum, or the squared magnitude of the Fourier transform of the data log-power spectrum, is commonly observed when processing reflections from plate-like structures, such as membranes. In this case, the cepstral peak at the smallest nonzero time lag, or quefrency, value can be used to determine the thickness of the plate. For reflections from a medium composed of randomly distributed scatterers, such as liver tissue, a cepstral peak is also commonly observed, but cannot be so intuitively explained as in the deterministic case above. In this paper, it is demonstrated that the presence of a cepstral peak depends on the form of the probability density function (pdf) of the separation between reflectors. In the case where the pdf is uniform from O to SM, the cepstral peak is found to occur at the quefrency corresponding to SM. For simple unimodal pdfs, a cepstral peak will occur at the location of the maximum probability. These observations are shown analytically and verified through simulations. The diagnostic value of these results lies in the interpretation of the relation of the cepstral peak location to the spacing of the scattering elements in the tissue.
在处理来自板状结构（如膜）的反射时，通常会在功率倒谱（即数据对数功率谱的傅里叶变换的平方幅度）中观察到一个峰值。在这种情况下，最小非零时间延迟（即倒频率）值处的倒谱峰值可用于确定板的厚度。对于来自由随机分布的散射体组成的介质（如肝组织）的反射，也通常会观察到一个倒谱峰值，但不像上述确定性情况那样可以直观地解释。本文证明，倒谱峰值的存在取决于反射器之间间距的概率密度函数（pdf）的形式。在pdf从0到SM均匀分布的情况下，发现倒谱峰值出现在对应于SM的倒频率处。对于简单的单峰pdf，倒谱峰值将出现在最大概率的位置。通过分析展示了这些观察结果，并通过模拟进行了验证。这些结果的诊断价值在于解释倒谱峰值位置与组织中散射元件间距的关系。
