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An Integral Inequality Bounding the Autocorrelation of a Pulse or Sequence at a Known Lag  
 
  Authors: Robin Willink,  
  Keywords: Inequalities, Auto-correlation, Bounds.  
  Date Received: 17/07/01  
  Date Accepted: 05/11/01  
  Subject Codes:

26D15,26D07.

  
  Editors: Pietro Cerone,  
 
  Abstract:

This paper gives best bounds for the ratio $ int^{b-t}_a f(x) f(x+t) dx/int^b_a f^2(x) dx$ for any square-summable real function $ f(x)$ on the interval $ (a,b]$. 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.;


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