Design of Finite Impulse Response Low-Pass Digital Differentiators for Signals in Paley-Wiener Space

Linear Finite Impulse Response (FIR) models for signals in Paley-Wiener space are developed in this thesis. A set of FIR models are derived where the filter coefficients only depend on the bandwidth and the sampling interval. There exists an anti-symmetry in the filter coefficients among different models and within the same model due to the location of the approximation point. By utilizing the symmetry, the computational cost for the filter coefficients is significantly reduced. The FIR model is also used in the reconstruction of a signal from its integral samples, which has applications in digital signal processing. A closed form bound on the error of approximation of FIR models is obtained, and the effectiveness of the proposed models is also demonstrated through numerical experiments