Sampling of periodic signals: A quantitative error analysis
Journal
IEEE Transactions on Signal Processing
Journal Volume
50
Journal Issue
5
Date Issued
2002-05-01
Author(s)
Abstract
We present an exact expression for the L 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.
Subjects
Asymptotic performance | Curves | Error bounds | Periodic representations | Sampling
Type
journal article