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Methods for designing two types of periodic ternary input signal used to identify a system in the presence of both noise and nonlinear distortions have been described here. Signals of the first type have even harmonics suppressed, to eliminate errors in odd-order estimates from even-order distortions, and vice-versa. Signals of the second type have harmonic multiples of both two and three suppressed, to further reduce errors from nonlinear distortions. For both types of signal, three design criteria are defined. The first criterion allows the signal energy-amplitude ratio to be maximised, the second allows the signal spectrum uniformity to be maximised and the third allows a compromise to be made between the first two criteria. With the methods described, ternary signals of both types with a very wide range of periods can be obtained for use in this application. Software for computer-aided design of the signals is available on the Internet. The signals and their periods are given in tables, and an example is used to show how they are applied.