A note on transformed Fourier systems for the approximation of non-periodic signals.
2021
A variety of techniques have been developed for the approximation of non-periodic functions. In particular, there are approximation techniques based on rank-$1$ lattices and transformed rank-$1$ lattices, including methods that use sampling sets consisting of Chebyshev- and tent-transformed nodes. We compare these methods with a parameterized transformed Fourier system that yields similar $\ell_2$-approximation errors.
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