Quantisation Considerations in Digital Filter Implementation

Abstract

Digital filters have been successfully implemented using digital minicomputers^1,2, microprocessors^3,4 and dedicated hardware.⁵ The implementation of the filter involves, to some degree, using hardware having finite word lengths (16 bits, 12 bits or 8 bits are typical). These finite word lengths represent sampled-data input and output signals, filter coefficients and results of arithmetic computations; consequently inherent errors exist in the representation of these parameters, and they normally take the form of

• (1) quantisation errors which arise as a result of arithmetic computations (round off and truncation errors);

• (2) quantisation errors due to representing the input signal by a set of discrete values;

• (3) quantisation errors due to representing the filter coefficients by a finite number of bits;

• (4) limit cycle oscillations; and

• (5) overflow oscillations.

The design of the filter can be undertaken without detailed consideration of the effects of finite word lengths (see chapter 2 and chapter 3). However, in contrast, in the practical implementation of the filter the errors listed above in (1) to (5) inclusive, must be considered, and they must be eliminated or kept as small as possible.