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Earth and Space Sciences · 术语表

什么是 Periodogram?

Definition 16.10 University Earth and Space Sciences — Year 3 · 第 16 章 — Sequence Stratigraphy

The periodogram of a series y0,…,yN−1y_0, \dots, y_{N-1} sampled at a step Δ\Delta (in time or depth), after removal of its mean and trend and multiplication by a taper wkw_k, is

P(fj)=∣∑k=0N−1wkyk e−2πifjkΔ∣2,fj=jNΔ, j=1,…,N2:P(f_j) = \Bigl|\sum_{k=0}^{N-1} w_k y_k\, e^{-2\pi i f_j k\Delta}\Bigr|^2, \qquad f_j = \frac{j}{N\Delta},\ j = 1, \dots, \frac N2:

the power of the series at each frequency fjf_j, the square of the modulus of its discrete Fourier transform.

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