Floating-point to fixed-point conversion with decision errors due to quantization

Most existing analyses of quantization effects are given under the condition that all decision-making blocks, if they exist in a system, produce identical decisions in both fixed-point and infinite-precision (IP) implementations. However, in doing floating-point to fixed-point conversion (FFC), a fixed-point design with occasional decision errors may still be an acceptable approximation of the IP system. We study the effect of this decision error, and relate its probability to the fixed-point data types. Our previous FFC methodology is then extended to include systems with possible decision errors due to quantization. The extended approach is applied to both CORDIC and a BPSK transceiver.