New approaches to Fourier analysis of ammonoid sutures and other complex, open curves
New approaches to Fourier analysis of ammonoid sutures and other complex, open curves
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DOI：
10.1666/04042.1
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发表时间：
2006-03-01
期刊：
影响因子：
2.7
通讯作者：
Allen, EG
中科院分区：
文献类型：
--
作者：
Allen, EG
尝试使用傅立叶方法量化菊石缝线形状未能产生稳健的可重复结果，因为缝线是违反傅立叶数学假设的复杂曲线。特别是，采样缝合线被人为截断，这样的第一个和最后一个采样点是不相等的，褶皱是非静止的，和一个位置沿着水平参考轴可以映射到多个振幅沿着的缝合path.here我介绍一种替代傅立叶方法的窗口短时傅立叶变换（STFT），它适应这些复杂曲线的特点。对于每根缝线，使用切线角度函数对数字化标志进行参数化，然后通过与切趾函数进行卷积进行平滑。然后计算逐段傅立叶变换并求平均值，从而得到线形态的鲁棒的、独特的量化。STFT系数和估计功率谱描述的谐波的相对权重产生的576古生代-三叠纪基菊石属，代表的缝合线形态类型的范围。虽然不敏感的分类营业额的主要事件（弗拉斯/法门期，末泥盆世，二叠纪/三叠纪），总功率数据支持以前观察到的趋势，随着时间的推移，增加缝合线的复杂性。此外，分区的总和功率统计到谐波范围允许新的洞察古生代缝合线的演化。特别是，数据显示显着的变化，在反弹和辐射期间的优势形态，并建议，基三叠纪菊石具有独特的缝合线形态相比，古生代。
Attempts to use Fourier methods to quantify ammonoid Suture shape have failed to yield robust, repeatable results because Sutures are complex Curves that violate the assumptions of Fourier mathematics. In particular, sampled sutures are artificially truncated Such that the first and last sampled points are not equivalent, the folds are non-stationary, and a position along a horizontal reference axis may map to multiple amplitudes along the Suture path. Here I introduce an alternative Fourier method-the windowed short-time Fourier transform (STFT)-that accommodates these characteristics of complex curves. For each suture, digitized landmarks were parameterized using a tangent angle function and then smoothed by convolving with an apodization function. Piece-wise Fourier transforms were then calculated and averaged, resulting in a robust, unique quantification of line morphology. STFT coefficients and estimated power spectra describing the relative weights of harmonics were generated for 576 Paleozoic-basal Triassic ammonoid genera, representative of the range of suture morphotypes. While insensitive to major episodes of taxonomic turnover (Frasnian/Famennian, end-Devonian, and Permian/Triassic extinctions), the summed power data support the previously observed trend toward increasing suture complexity through time. Moreover, partitioning the summed power statistic into harmonic ranges allows novel insight into Paleozoic suture evolution. In particular, the data show significant shifts in the dominant morphotypes during periods of rebound and radiation and suggest that basal Triassic ammonoids possessed unique Suture morphotypes when compared with those of the Paleozoic.