Cohen's class time-frequency representation in linear canonical domains: definition and properties

Abstract

The traditional Cohen's class time-frequency representation is extended to the linear canonical domain by using a well-established closed-form instantaneous cross-correlation function (CICF) type of linear canonical transform (LCT) free parameters embedded approach. The derived CICF type of Cohen's class (CICFCC) unifies some well-known Cohen's classes in linear canonical domains including the affine characteristic, basis function, convolution expression and instantaneous crosscorrelation function types of Cohen's classes, and can be considered as the Cohen's class's closed-form representation in linear canonical domains. A fundamental theory about the CICFCC's essential properties, such as marginal distribution, energy conservation, unique reconstruction, Moyal formula, complex conjugate symmetry, time reversal symmetry, scaling property, time shift property, frequency shift property, and LCT invariance, is then established. Possible applications are also carried out to illustrate that the CICFCC outperforms the traditional one in nonstationary signal separation and detection.