Fractional Time-Shift B-Spline Filter

The fractional time-shift operators are essential devices in processing and adjustment of signals in modern communication systems. This letter introduces the fractional time-shift B-spline filter. The filter produces a time-shift Delta isin [0,1], which is an arbitrary fraction of the sampling period. We describe the construction and parallel implementation of the fractional time-shift filter. We give several of its applications (differentiator, integrator, and correlator) in numerical and statistical signal processing and in adaptive time-shift adjustments.