The paper introduces a novel family of deterministic signals, the orthogonal periodic sequences (OPSs), for the identification of functional link polynomial (FLiP) filters. The novel sequences share many of the characteristics of the perfect periodic sequences (PPSs). As the PPSs, they allow the perfect identification of a FLiP filter on a finite time interval with the cross-correlation method. In contrast to the PPSs, OPSs can identify also non-orthogonal FLiP filters, as the Volterra filters. With OPSs, the input sequence can have any persistently exciting distribution and can also be a quantized sequence. OPSs can often identify FLiP filters with a sequence period and a computational complexity much smaller than that of PPSs. Several results are reported to show the effectiveness of the proposed sequences identifying a real nonlinear audio system.