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This paper deals with a novel time-interval measurement method that makes use of a surface acoustic wave (SAW) filter as a time interpolator. The method is based on the fact that a transversal SAW filter excited by a short pulse can generate a well-defined finite signal with highly suppressed spectra outside a narrow frequency band. If the responses to two excitations are sampled at clock ticks, they can be precisely reconstructed from a finite number of samples and then compared to determine the time interval between the two excitations. As a first step of a more comprehensive discussion of the method, the time-interpolation error caused by deterministic effects has been analyzed in this paper. It has been shown that the mean square of the interpolation error is limited by the upper bound, which is proportional to the relative energy of aliasing distortion and inversely proportional to the square of the filter center frequency. The upper bound has been compared to the results obtained from the simulation based on a linear-phase transversal filter. The RMS error resulting from the simulation exactly follows the slope of the theoretical upper bound, and it is approximately four times smaller than that. The described method excels in time interpolation efficiency since the time interpolation error relative to clock period is small; in other words, accurate measurement can be achieved even with a relatively low clock frequency. This has been practically demonstrated in a time-interval counter, which provides precision of 7-ps RMS using a clock frequency as low as 16.4 MHz. It results from the analysis that using state-of-the-art elements in the interpolator, the deterministic interpolation error on the order of 0.1 ps can be achieved.