Data Reduction
Digital systems often reduce the word length of a binary value by discarding the lowest order bits. Register truncation occurs when a high precision calculation result must be stored in a smaller memory location. This process differs from rounding because it always removes the lower bits without considering their value.
Quantization Error
Removing information from the signal path introduces a sawtooth shaped error function into the data. This error acts as a noise source that is often correlated with the signal itself, potentially creating unwanted harmonics. In feedback control loops, the accumulation of these small errors can lead to limit cycles or instability.
Hardware Constraint
Fixed point processors use this method because it requires no additional logic beyond simple bit selection. Compared to convergent rounding, the hardware cost is zero. Designers must ensure that the remaining bit depth provides enough resolution to meet the system requirements.
Signal Fidelity
Dithering techniques sometimes precede the reduction to spread the truncation noise across the spectrum. By adding a small amount of random noise, the correlation between the signal and the error is broken. This improves the effective linearity of the system at the cost of a slightly higher overall noise floor.
