Volume 3,
Issue 1, 2002
Article
15
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AN INTEGRAL INEQUALITY BOUNDING THE AUTOCORRELATION OF A PULSE OR SEQUENCE AT A KNOWN LAG
ROBIN WILLINK
APPLIED MATHEMATICS
INDUSTRIAL RESEARCH LTD
PO BOX 31-310, LOWER HUTT
NEW ZEALAND
E-Mail: robin@weka.grace.cri.nz
Received 17 July, 2001; 05 November, 2001.
Communicated by: P. Cerone
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for any square-summable real
function 
on the interval ![$ (a,b]$](../abstract/057_01_ab/img3.gif){kind=small}
. Similarly, bounds are
established for the autocorrelation of any pulse or finite-length
sequence at any known lag, and the family of pulses and sequences
attaining these bounds is identified. The form of this family is
related to a half-cycle of a sinusoid. Stronger bounds are suggested for
pulses known to be non-negative and unimodal or concave.