On the reconstruction of derivative sampling method of band-limited signal

In this paper, the reconstruction methods of the derivative sampling methods of bandlimited signals are presented. First, the conventional Nyquist uniform sampling method and the derivative sampling method are reviewed briefly. Then, the reconstruction filters are designed by converting the analog filter bank structure in derivative sampling method to an equivalent discrete-time filter bank structure preceded by Nyquist uniform sampling and followed by impulse modulation and lowpass filtering. Next, the first-order derivative sampling method is extended to fractional-order derivative sampling method and the designs of its reconstruction filter bank are also studied. To reduce the implementation complexity, the orthogonal matching pursuit method is used to design the sparse digital filter bank in the proposed reconstruction structure. Finally, some numerical examples are used to show the effectiveness of the proposed reconstruction methods of the derivative sampling schemes.