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A note on Unser-Zeruhia generalized sampling theory applied to the linear interpolator

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2 Author(s)
Janssen, A. ; Philips Res. Lab., Eindhoven, Netherlands ; Kalker, T.

In this correspondence, we calculate the condition number of the linear operator that maps sequences of samples f(2k), f(2k+a), k∈Z of an unknown continuous f∈L2 (R) consistently (in the sense of the Unser-Zeruhia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a∈(0,2). It turns out that the minimum condition numbers occur at a=√2/3 and a=2-√2/3 and not at a=1 as we might have expected. The theory is verified using the example of video deinterlacing

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Signal Processing, IEEE Transactions on  (Volume:47 ,  Issue: 8 )