Sinc interpolation errors in finite data record length

Sinc (Sin(x)/x) interpolation is widely used in the test and measurement community because of its ease of use. It is also well known that, in practice where only finite length of data record are available, there are substantial errors near the end of the data record due to Gibbs' phenomenon. In this paper we examine this phenomenon in more detail and quantify errors in such a way to provide some quick and simple rules for estimating the maximum error. It is shown that the largest interpolation error, which occurs at the middle of the first interpolation interval, has its magnitude dependent on both the amount of the discontinuity and the slope of the signal at the discontinuity. For a low frequency (as compared to the sampling frequency) signal the peak error magnitude is about 14% of the amount of the discontinuity. For high frequency signals, the peak error depends heavily on how the first few missing data points correlating to the sinc kernel. As frequency approaches the Nyquist frequency, the error grows unbounded. We also show that the peak error magnitude in each subsequent interpolation interval will decrease, approximately, by the factor of 3/(2m+l) at the m-th interpolation interval counting from the edge of the data record.<
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