An iterative LMI algorithm for quantization noise reduction in ΔΣ modulators

In this paper, we design noise shaping filters for quantization noise reduction in ΔΣ modulators. The design problem for the noise shaping infinite impulse response (IIR) filter in the feedback of the ΔΣ modulator is in non-convex form, which is hard to solve in general. We propose an iterative linear matrix inequality (LMI) algorithm to find a near optimal noise shaping IIR filter by solving the non-convex design problem. The least-squares and the hybrid design are two methods, either of which can serve as a starting point for our iterative LMI algorithm to obtain a near optimal solution. We also compare and analyze the performances of some other noise shaping techniques with our proposed algorithm. A design example for a bandpass ΔΣ modulator based radio frequency transmitter is provided which takes into account the non-ideal behavior of the output analog filter.