Optimal Least-Squares Design of Sparse FIR Filters for Big-Data Signal Processing

Since amount of big data is extremely huge, low delay and low-complexity signal processing devices are strongly required in big data signal processing. Digital filters are the key device for digital signal processing. Digital filters with sparse coefficients (0 coefficients) are beneficial to reduce the computational complexity. This paper proposes a design method for low-delay FIR filters with sparse coefficients. We consider the optimization of combination of selection for sparse coefficients. If the sparse coefficients are selected, the real coefficients can he computed based on the Lagrange multiplier method. We employ the branch and bound method incorporated with the Lagrange multiplier method. Also, we propose a selection method of the initial cost for high-speed search. The feature of this method is as follows: (a) The number of 0 coefficients can explicitly specify. (b) The optimality is guaranteed in the least squares sense. We present a design example in order to demonstrate the effectiveness of our method.