At spectral radius 1, the feature-space motifs of a linear Simple Cycle Reservoir are exactly the sampled Fourier basis vectors.
Simple Cycle Reservoirs are Universal
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Linear Simple Cycle Reservoirs at the edge of stability perform Fourier decomposition of the input driving signals
At spectral radius 1, the feature-space motifs of a linear Simple Cycle Reservoir are exactly the sampled Fourier basis vectors.