Design of sparse lowpass differentiator using iterative hard thresholding method

In this paper, the design of a sparse digital lowpass differentiator is presented. First, the original iterative hard thresholding (IHT) algorithm in the compressed sensing is used to solve this design problem. Then, a modified IHT algorithm is proposed to improve the performance by using a smooth thresholding technique. Finally, the proposed IHT methods are compared with the conventional orthogonal matching pursuit (OMP) method to show their performance. The main feature of the proposed design methods is that the error of magnitude response and sparsity of filter coefficients can be controlled by suitably choosing the thresholding parameter.