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This paper offers an alternative odd-quantisation approach scheme for Cartesian ΔΣ systems proposed for the all-digital upconversion of baseband modulation to radio frequency (RF). The developed Cartesian ΔΣ system with even-quantisation has a minimum pulsewidth of two clock periods. This leads to a potential coarse quantisation at low signal levels. We show that the noise problem can be reduced with a new odd-quantisation scheme which is based on pulses with an odd number of clock periods. In this paper, the minimum pulsewidth is reduced to one clock period. Other quantized amplitudes are obtained by incrementing the pulsewidth in steps of two clock periods, which maintains a constant phase reference. In both cases separate quantisers for amplitude and phase enable simple implementation. We show that both odd and even-quantisation schemes produce the same distortion products that increase with frequency offset. The odd-quantisation scheme, however, has improved SNR by approximately 2 dB.