Derivative Sampling of Periodic and Nonperiodic Band-Limited Signals — Fourier Spectrum and Interpolation Formula

For periodic and nonperiodic band-limited signals, the sampling of both the signal and the signal derivative enables the number of sampling points to be reduced and the sampling step between the sampling points, thus, increased by a factor of 2 compared to the standard Nyquist-Whittaker–Shannon-Kotelnikov–Someya sampling theorem. This article presents closed-form expressions for the Fourier spectra and the interpolation formulas based on sampling of signal and signal derivative; the expressions for periodic signals are exact, whereas the expressions for nonperiodic signals are necessarily approximate due to the unavoidable truncation error.