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Exact reconstruction of sparse non-harmonic signals from their Fourier coefficients

2021
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Sampling Theory, Signal Processing, and Data Analysis
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AbstractIn this paper, we derive a new reconstruction method for real non-harmonic Fourier sums, i.e., real signals which can be represented as sparse exponential sums of the form $$f(t) = \sum _{j=1}^{K} \gamma _{j} \, \cos (2\pi a_{j} t + b_{j})$$ f ( t ) = ∑ j = 1 K γ j cos ( 2 π a j t + b j ) , where the frequency parameters $$a_{j} \in {\mathbb {R}}$$ a j ∈ R (or $$a_{j} \in {\mathrm i} {\mathbb {R}}$$ a j ∈ i R ) are pairwise different. Our method is based on the recently proposed

doi:10.1007/s43670-021-00007-1
fatcat:bnpn37ykazhcze4oyudyxq5sqa