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Sampling of periodic signals: A quantitative error analysis
Journal article   Open access   Peer reviewed

Sampling of periodic signals: A quantitative error analysis

Mathews JACOB, Thierry BLU and Michael UNSER
IEEE transactions on signal processing, Vol.50(5), pp.1153-1159
2002
DOI: 10.1109/78.995071
url
https://doi.org/10.1109/78.995071View
Published (Version of record) Open Access

Abstract

We present an exact expression for the L/sub 2/ error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schemes including wavelets, splines, and bandlimited signal expansions. The formula takes the simple form of a Parseval's-like relation, where the Fourier coefficients of the signal are weighted against a frequency kernel that characterizes the approximation operator. We use this expression to analyze the behavior of the error as the sampling step approaches zero. We also experimentally verify the expression of the error in the context of the interpolation of closed curves.
Applied Sciences Signal and communications theory Sampling, quantization Information, signal and communications theory Telecommunications and information theory Exact sciences and technology

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