The thesis begins with an overview of the four types of error that are generated in digital filters
which arise from two sources. The first source is the quantisation of time through the sampling
process which gives rise to the first error type - algorithmic error. The second source of error
is the quantisation of amplitude due to finite wordlength effects. Coefficient representation
error (coefficient error), ADC quantisation error (ADC error) and multiple-word truncation
error (truncation error) are all effects of amplitude quantisation.
The shift operator commonly used in digital filters is prone to sensitivity problems especially
at high sampling rates. Alternative filter operators are reviewed and advantages and
disadvantages of their use are identified in enhancing the performance of digital filters.
The measurement of algorithmic error and coefficient error can be carried out deterrninistically
whilst ADC error and truncation error need to be treated stochastically. The thesis presents a
technique to separate the deterministic error and the stochastic error in a composite output
signal from a digital filter that is implemented using a high-Ievellangnage with floating-point
arithmetic. This technique represents a method for validating the error analysis techniques.
The error analyses presented in the thesis are used as tools to improve the performance of
emulated digital filters. Each different error form varies in an individual manner with respect
to changes in the sampling period. By careful selection of a sampling rate the filter
performance can be improved by ensuring that the magnitudes of all the error forms are
consistent with each other.
Similar techniques can be used to improve the performance of digital compensators in c1osedloop
control systems. Careful consideration of the duration of the sampling interval needs to
be observed to ensure that the stability of the closed-loop system is adequate. This method of
determining the controller parameters is used to exploit the digital control hardware to its
fullest potential, and is automated in software; details are described in the thesis.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.