Ramanujan-sums have in the past been used to extract hidden periods. In a recent paper it was shown that for finite duration (FIR) sequences, the traditional representation is not suitable. Two new types of Ramanujan-sum expansions were proposed for the FIR case, each offering an integer basis, and applications in the extraction of hidden periodicities were developed. Crucial to these developments was the introduction of Ramanujan spaces. The aim of this paper is to develop some properties of these subspaces in the context of signal processing. The design of near orthogonal bases for these spaces is emphasized.
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