A Guide on Spectral Methods Applied to Discrete Data in One Dimension

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/jam/volume-2017/5108946/figures/5108946.fig.0014a.svgz" name="5108946.fig.0014a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Time domain</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/jam/volume-2017/5108946/figures/5108946.fig.0014b.svgz" name="5108946.fig.0014b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Waterfall diagram</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/jam/volume-2017/5108946/figures/5108946.fig.0014c.svgz" name="5108946.fig.0014c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>1D spectrum</td></tr></table>

<div>Complex example for the temporal-dependent spectral decomposition. (a) shows the time series and (b) its decomposition. Panel (c) demonstrates that the simple 1D spectrum would produce misleading results. Here one can only identify the 10 Hz carrier, but the frequency drift is hidden behind the wide band spectrum at around 30 Hz.</div>

Journal of Applied Mathematics

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Figure 14

Figure 14: A Guide on Spectral Methods Applied to Discrete Data in One Dimension 