Title :
On the autocorrelation of finite-length sequences
Author :
Steinhardt, Allan O. ; Makhoul, John
Author_Institution :
Massachusetts Institute of Technology, Lexington, MA, USA
fDate :
12/1/1985 12:00:00 AM
Abstract :
lt is well known that all autocorrelation sequences are positive (semi)definite. The correlation sequence is further constrained when, as is often the case, it is obtained from correlating a finite-length data sequence with itself. In this paper we study the effect of the data sequence length on the attainable correlations. We derive a formula for the sequence length needed to match an autocorrelation value at a given lag. The formula indicates that inordinately long sequences are needed to obtain a normalized autocorrelation coefficient near unity. We conclude that all-zero (moving-average) models may be ill suited for highly correlated signals. The formula for the single-lag case is then used to obtain a bound on the sequence length needed to match a set of autocorrelations simultaneously.
Keywords :
Autocorrelation; Helium; Laboratories; Lagrangian functions; Signal processing;
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
DOI :
10.1109/TASSP.1985.1164758