In this paper we present a correlation based error estimation technique using a residual test signal for the linearization of multibit feedback DACs of lowpass and bandpass Delta-Sigma analog-to-digital converters. Using residual test signal insertion allows operating in background with only limited loss in peak performance during test. Opposed to dynamic element matching techniques, which are limited by the intrinsic nonlinearities in the feedback DAC, the presented method recovers the performance of highly nonlinear systems back to their ideal resolution.