This paper proposes an analytical method to directly synthesise pseudo-random ternary perturbation signals for the identification of frequency response functions, through the multiplication of two components signals which satisfy a prescribed set of properties. The ternary signals generated have harmonic multiples of two and three suppressed; this specification is useful for reducing the effects of nonlinear distortion on the linear estimate. The signals have uniform magnitude in all, except two, of the nonzero harmonics. The method is significant in overcoming the existing problem of sparsity in the available periods when analytical methods are used, as well as the relatively long computational time required in approaches based on exhaustive search or computer optimisation. The proposed technique presents a breakthrough as it eliminates the sequence-to-signal conversion stage required in the existing conventional methods. A direct consequence is the increased signal power within amplitude constraints, which now equals the theoretical limit for the specification considered. If it is necessary to further increase the number of available periods, the mathematical derivation can be extended to a class of suboptimal direct synthesis signals; however, these possess reduced signal power compared with direct synthesis signals. (C) 2013 Elsevier Ltd. All rights reserved.