The Interpolation of Sparse Time History Data

Improvements in signal-aliasing protection in modern digital data acquisition systems allow the collection of discrete data at sample rates that are very close to the theoretical limit of two times the desired data bandwidth. This produces very high "efficiency" in the acquisition process and very good fidelity and near-optimum bandwidth for spectral measurements. However, the resulting time-history data is very sparse and must be processed in order to reconstruct the waveform. A number of techniques to calculate the intermediate values have been described in the literature. One of them, that can be implemented by many of the data processors available, is to use zero-insertion in the spectral domain-a method that works perfectly for signal segments that do not have significant energy at the Nyquist frequency. Unfortunately, most signals that are to be interpolated do not satisfy this condition and significant errors result. This paper describes an extension to the zero-insertion technique that uses "windowed guard bands" to reduce the errors to acceptable levels. The interrelationship between sample ratio, interpolation ratio, window used, and guard-band size is examined and their effect on errors is discussed. A procedure that assures errors of less than .1% of full scale is described.

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