Analysis of the quantization error in digital multipliers with small wordlength

The analysis of the quantization error in fixed-point arithmetic is usually based on simplifying assumptions. The quantization error is modelled as a random variable which is independent of the quantized variable. This contribution investigates the wordlength reduction of a digital multiplier in greater detail. The power spectrum of the quantization is expressed by the power spectrum of the multiplier input. The analytical results agree with measurements of the quantization error. The presented error model is shown to be superior to the simplified one for wordlengths in the range of eight bit.