Multichannel Interpolation for Periodic Signals via FFT, Error Analysis and Image Scaling

This paper describes a new method for the multichannel interpolation of a discrete signal. It is shown that a bandlimited periodic signal $f$ can be exactly reconstructed from finite samples of $g_k$ ($1\leq k\leq M$) which are the responses of $M$ linear systems with input $f$. The proposed interpolation can also be applied to approximate non-bandlimited periodic signals. Quantitative error analysis is provided to ensure its effectiveness for approximating non-bandlimited periodic signals and its Hilbert transform. Importantly, involving the fast Fourier transform (FFT) computational technique, bring high computational efficiency and reliability of the proposed algorithm. The superior performance of the proposed algorithm is demonstrated by several simulations. Additionally, the proposed interpolation is applied to the image scaling problem. The empirical studies show that the proposed method performs better than the other conventional image scaling methods.

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