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Notes
- 1.
Obviously, since the moiré cluster is a subset of the overall spectrum, its structure can never be more complex than that of the overall spectrum.
- 2.
This additive behaviour of the impulse amplitudes should not be confused with the multiplicative behaviour of the individual impulse amplitudes in the convolution process: Each individual impulse amplitude in the convolution is obtained by Eq. (2.27) as a product; but if several impulses thus obtained happen to fall on the same geometric location, their individual amplitudes are then summed.
- 3.
The s-th 1D cluster in the spectrum consists of the impulses: (n,−n) + (s,0) = (n−s, s−n) + (s,0) = (n, s−n) for all n ∊Z; as we have seen in Sec. 5.6.2, these impulse-indices are a translated version of the impulse-indices (n,−n) of the main, 0-th cluster.
- 4.
Cases in which the set of all collapsed-down clusters is not a lattice but rather a dense module will be discussed in the next section.
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© 2009 Springer-Verlag London Limited
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Amidror, I. (2009). Fourier-based interpretation of the algebraic spectrum properties. In: Amidror, I. (eds) The Theory of the Moiré Phenomenon. Computational Imaging and Vision, vol 38. Springer, London. https://doi.org/10.1007/978-1-84882-181-1_6
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DOI: https://doi.org/10.1007/978-1-84882-181-1_6
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