The design of pseudo-random maximum length (PRML) ternary signals with properties suitable for identification of generalized quadratic. Hammerstein models is considered. For such an application, it is desirable for the signal to have odd harmonics uniform and even harmonics suppressed, with its squared version having odd harmonics suppressed and even harmonics uniform. To date, the only class of signal known to possess such harmonic properties comprises of PRML ternary signals based on Galois field GF(3), and its extension fields. In this note, theoretical conditions for a PRML signal to possess these properties are derived and imposed on the design of signals based on higher odd fields to generate truncated PRML signals that fulfill the required specifications.