Design of noise shaping FIR filters by minimizing in-band peak amplitude for stable single- and multi-bit data converters

This paper presents an optimal design of noise-shaping FIR filters for single- and multi-bit data converters. In the design, only three parameters, the number of taps, oversampling ratio (OSR) and l₁-norm of the coefficients are first specified, and the in-band peak of the amplitude response is directly minimized under the specification. Also the out-of-band amplitude can be weighted and shaped. In design examples, many noise-shaping FIR filters that can be used in single- and multi-bit data converters are designed by the optimal method, and their performance limits are addressed. Also the paper presents a heuristic design to reduce computational cost of the optimization. For single-bit data converters with OSR 128, a noise-shaping FIR filter is designed by the heuristic method and then shown to achieve an SNDR 132dB and perform a noise suppression of at least 117dB in the band of interest.