The time-domain reconstruction method of Giannakis [J. Opt. Soc. Am. A 6, 682 (1989), Subsec. 3.B] is correct and was derived under the assumption that a matrix containing certain triple-correlation lags has full rank. Although the counterexample of Tugnait [J. Opt. Soc. Am. A 8, 452 (1991)] violates this assumption, I show that a full-rank triple-correlation matrix exists. Recent important results that establish a unique reconstruction of two-sided polezero signals and their orders are also presented.
© 1991 Optical Society of America
Georgios B. Giannakis, "Signal reconstruction from multiple correlations: frequency- and time-domain approaches: reply to comment," J. Opt. Soc. Am. A 8, 454-455 (1991)