Optimal input design using generalized binary sequence

Abstract

The generalized binary sequence (GBS) of Tulleken offers an attractive alternative in input design for system identification. In terms of time-domain responses, the GBS ranges from a square-wave sequence to a step input as the non-switching probability changes from zero to unity. In terms of frequency responses, the emphasis of input spectrum changes from low frequency to the Nyquist frequency as the non-switching probability varies. In this work, analytical expression for the optimal non-switching probability for the GBS is derived when the specification is given on a single-frequency value. Moreover, for a more realistic case, if the specification is given as a frequency interval, the optimal non-switching probability can also be obtained analytically. A linear example is used to illustrate this GBS-based input design procedure.