Page 411 - Analog and Digital Filter Design

408 Analog and Digital Filter Design

to introduce instability. Rounding of coefficient values occurs when a fixed-point
DSP device is being used.

An 8-bit data word produces a coefficient range of f 128 levels, a step increment
of 0.0078125. A 16-bit data word produces a coefficient range of f 32768 levels;
this time the step increment is reduced to about 0.0000305176. As the data word
length increases, the risk of instability reduces because rounding up or down to
a step increment level will be little different from the original value. Floating-
point DSP devices have the advantage of being able to use more precise coeffi-
cients and are therefore less likely to introduce instability.

Reference

1. Cunningham, E. P. Digital Filtering: An Introduction. Boston: John
Wiley & Sons, 1992.