A pair of quadriphase sequences whose aperiodic auto and cross-correlation functions take pure imaginary values

Orthogonal sequences (Fan and Darnell, 1997), whose periodic auto-correlation functions take zero for non-zero shifts, have been discussed for spread spectrum communication and radar. For such applications, it is desirable to use an optimal sequence whose aperiodic auto-correlation function takes zero for non-zero shifts, since a matched filter which takes correlation between it and a received signal obtains an impulse response, even if the inverse sequence is often sent. However there does not exist such a sequence. This paper presents a pair of quadriphase sequences, whose aperiodic auto-correlation functions for non-zero shifts and cross-one for any shift take pure imaginary values. It looks as if each output of matched filters is impulsive at any time, when only the real part of the correlation is extracted.