Effects of Finite Wordlength

Abstract

In this chapter, quantization effects, the quantization errors due to the limitation of wordlength in digital filters and DFT algorithms, are analyzed. As the noise signal due to quantization is of random nature, the quantization noise is modeled using probability theory. Some assumptions are made to make the model relatively simpler one. The analysis is carried out to find the adequate wordlength that will make the digital filter work with a high signal-to-noise ratio. The DFT algorithm reduces the noise of the previous stage by the scaling factor, and the resulting noise is much smaller at the output. In the digital filters, coefficient quantization results in changing the frequency response due to the movement of poles and zeros of the transfer function. The round-off noise due to truncation or rounding in multiplication operations reduces the signal-to-noise ratio at the output. Further, the assumed linear noise model becomes sufficiently nonlinear to produce spontaneous oscillations called limit cycles. All the unwanted effects due to quantization get reduced as the wordlength is increased. Although the models indicate the effects due to quantization to a good extent, the best analysis of these effects is by simulation.