Dynamic ElementMatching (DEM) techniques for Digital-to-Analog Converters (DACs) is an effective approach to achieving good linearity in an oversampling Delta Sigma Modulator (DSM). There are different DEM implementation algorithms from which, Data weighted averaging (DWA) is more suitable due to its reasonable good performance and hardware efficiency. However, it suffers seriously from itself tonal behavior lead to few differently modified structures. Furthermore, decreasing Over Sampling Ratio (OSR) limits its performance. In this case it can be applied together with another similar technique for example Noise Shaping Dynamic Element Matching (NSDEM). This paper, describes a BandPass DEM strategy dedicated to a low OSR Discrete Time Delta Sigma Modulator (DTDSM), which is a well combination of a modified tone free partitioned Data WeightedAveraging (DWA) alongside employing NSDEM technique. The proposed mismatched shaping method achieve a considerably better performance for a low OSR fourth order bandpass multibit Delta Sigma modulator and remove DAC nonlinearity error. The simulation results confirm theoretical aspects. This proposed technique improves both SNDR and SFDR of the DAC, reaching their ideal values.