Design of sparse digital differentiator using orthogonal matching pursuit method

In this paper, a new method is presented to design the sparse digital differentiator which is useful to determine and estimate the derivatives of given signal. First, the design problem is formulated a constrained ℓ₀ minimization problem. Then, the orthogonal matching pursuit algorithm is used to solve this optimization problem efficiently. As a result, the sparsity of filter coefficients and error of magnitude response can be controlled by suitably choosing the prescribed design parameter. Finally, several examples are demonstrated to show the effectiveness of the proposed design method.