Identification of direction-dependent processes using maximum length ternary signals

Abstract

Analytical results have been obtained for first-order direction-dependent processes perturbed using maximum length ternary (MLT) signals. In particular, the process output and the input-output crosscorrelation function are derived, leading to a theoretical expression for the combined time constant of the process. The importance of doing this is that the direction-dependent behaviour can be detected, and the combined linear dynamics of the process can be estimated, from the input-output crosscorrelation function. In the above derivations, it is assumed that the process dynamics are faster in the upward direction, and that the clock-pulse interval is chosen such that the output always decreases when the input is at signal level zero. The first of these assumptions does not affect the terms in the crosscorrelation function because the input signal is inverse-repeat. The second assumption is shown to be valid during most of the signal period. The errors caused by the deviation from the ideal case are assessed, and are found to be small. Hence, the ideal case can be used as an effective benchmark against which results from an identification test as specified above can be measured. Advantages and disadvantages of using the MLT signal, instead of the maximum length binary or its inverse-repeat signal, are discussed. A simulation example is also shown to verify the obtained theoretical results.