Digital Filter Design with State Space Method for 1-Bit Signal Processing Based on Delta-Sigma Modulation

Abstract

1-bit signal processing based on delta-sigma modulation has been studied for hardware implementation of signal processng systems. In the 1-bit signal processing, finite word-length problems such as overflow and coefficent quantization error occur. To solve the problems, new design method with state space is proposed in this paper. Digital filters are designed to show the feasibility of the method. Firstly, L₁/L₂-sensitivity is shown to evaluate coefficient quantization error and L₂ scaling constraints to prevent overflow. Secondly, state space equation is shown and L₁/L₂-sensitivity and L₂-scaling constraints are extended to take filter structure and oversampling effects into account. Finally, the proposed method is shown to attain higher SNR than conventional ones.