Fractional correlation operation: performance analysis

Abstract

The fractional correlation is a new tool related to the fractional Fourier transform. It is useful for comparison and recognition, especially for shift-variant cases. The performances of such a correlator are analyzed according to the standard criteria of signal-to-noise ratio, correlation sharpness (peak-to-correlation energy), and Horner efficiency. The conclusions are that the performance is object dependent and that for nonwhite noise, compared with the conventional correlator, improved performances are possible. In addition we show that for a white-noise spectrum the fractional correlation has performances similar to the conventional correlator.