Based on the definition of the instantaneous frequency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fra...

Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed an...

As the one-dimensional (1-D) Fourier transform can be extended into the 1-D fractional Fourier transform (FRFT), we can also generalize the two-dimensional (2-D) Fourier transform. Sahin et al. have generalized the 2-D Fourier transform into the 2-D separable FRFT (which replaces each variable 1-D Fourier transform by the 1-D FRFT, respectively) and 2D separable canonical transform (further rep...

We address numerical dispersion compensation based on the use of the fractional Fourier transform (FrFT). The FrFT provides a new fundamental perspective on the nature and role of group-velocity dispersion in Fourier domain OCT. The dispersion induced by a 26 mm long water cell was compensated for a spectral bandwidth of 110 nm, allowing the theoretical axial resolution in air of 3.6 μm to be r...

In this paper, we formulate the problem of sampling sparse signals in fractional Fourier domain. The fractional Fourier transform (FrFT) can be seen as a generalization of the classical Fourier transform. Extension of Shannon’s sampling theorem to the class of signals which are fractional bandlimited shows its association to a Nyquist-like bound. Thus proving that signals that have a non-bandli...

Security is one of the most challenging aspects in internet and Multimedia applications. Encryption is a process which is used to secure data. The Encryption algorithms and suitable transforms play a crucial role to form efficient security systems. In this regard the original information in the existing security system based on the fractional Fourier transform (FRFT) is protected by only a cert...