Application of linear canonical transform correlation for detection of linear frequency modulated signals

Linear canonical transform (LCT), which can be deemed to be a generalisation of the fractional Fourier transform, has been used in several areas, including signal processing and optics. Motivated by the operator theory, a new unitary operator associated with the LCT is introduced. This new operator generalises the unitary fractional operator which is proposed by Akay et al. recently. Via operator manipulations, the authors also derive a new definition, the LCT correlation operation, and present an alternative and efficient implementation of it. It is shown that the proposed LCT autocorrelation corresponds to radial slices of the ambiguity function in the ambiguity plane. On the basis of this relationship, an application of the fast LCT autocorrelation for detection and parameter estimation with respect to the chirp rates of linear frequency modulated signals corrupted by noise is proposed. Finally, the validity of the proposed method is verified by simulation results.