Min–Max Design of Error Feedback Quantizers Without Overloading

In this paper, we design a no-overloading error feedback quantizer based on a AΣ modulator, composed of an error feedback filter and a static quantizer. To guarantee no-overloading in the quantizer, we impose an l_∞ norm constraint on the feedback signal in the quantizer. Then, for a prescribed l_∞ norm constraint on the error at the system output induced by the quantizer, we design the error feedback filter that requires the minimum number of bits that achieves the constraint. Next, for a fixed number of bits for the quantizer, we investigate the achievable minimum l_∞ norm of the error at the system output with the no-overloading quantizer. Numerical examples are provided to validate our analysis and synthesis.