非周期信号近似的变换傅里叶系统的注记
A note on transformed Fourier systems for the approximation of non-periodic signals
摘要：
已经开发了各种技术来近似非周期函数。具体地，存在基于秩- $1$格和变换的秩- $1$格的近似技术，包括使用由切比雪夫变换和帐篷变换的节点组成的采样集的方法。我们比较这些方法与参数化变换傅立叶系统，产生类似的$\ell_2$近似误差。
英文摘要：
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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