Face recognition based on discriminant fractional Fourier feature extraction
Pattern Recognition Letters
Multicomponent chirp signals analysis using product cubic phase function
Digital Signal Processing
Time delay estimation using fractional Fourier transform
Signal Processing
New sampling formulae related to linear canonical transform
Signal Processing
The fan-chirp transform for non-stationary harmonic signals
Signal Processing
Sliding discrete fractional transforms
Signal Processing
Sampling rate conversion for linear canonical transform
Signal Processing
Time--frequency feature representation using energy concentration: An overview of recent advances
Digital Signal Processing
Image encryption with multiorders of fractional Fourier transforms
IEEE Transactions on Information Forensics and Security
Challenge-response-based biometric image scrambling for secure personal identification
Future Generation Computer Systems
Helicopter radar return analysis: Estimation and blade number selection
Signal Processing
Sampling random signals in a fractional Fourier domain
Signal Processing
The fractional Fourier transform and quadratic field magnetic resonance imaging
Computers & Mathematics with Applications
The fractional Fourier transform over finite fields
Signal Processing
Future Generation Computer Systems
On Convolution and Product Theorems for FRFT
Wireless Personal Communications: An International Journal
Fractional Fourier transform: a survey
Proceedings of the International Conference on Advances in Computing, Communications and Informatics
Speech recovery based on the linear canonical transform
Speech Communication
Discrete fractional wavelet transform and its application to multiple encryption
Information Sciences: an International Journal
Fractional Fourier transform based features for speaker recognition using support vector machine
Computers and Electrical Engineering
Rotation Invariance in 2D-FRFT with Application to Digital Image Watermarking
Journal of Signal Processing Systems
Subsample time delay estimation of chirp signals using FrFT
Signal Processing
The generalized continuous wavelet transform associated with the fractional Fourier transform
Journal of Computational and Applied Mathematics
A robust security framework for 3D images
Journal of Visualization
Doppler Estimation from Echo Signal Using FRFT
Wireless Personal Communications: An International Journal
Hi-index | 35.68 |
The functional Fourier transform (FRFT), which is a generalization of the classical Fourier transform, was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community, to which it may, however, be potentially useful. The FRFT depends on a parameter α and can be interpreted as a rotation by an angle α in the time-frequency plane. An FRFT with α=π/2 corresponds to the classical Fourier transform, and an FRFT with α=0 corresponds to the identity operator. On the other hand, the angles of successively performed FRFTs simply add up, as do the angles of successive rotations. The FRFT of a signal can also be interpreted as a decomposition of the signal in terms of chirps. The authors briefly introduce the FRFT and a number of its properties and then present some new results: the interpretation as a rotation in the time-frequency plane, and the FRFT's relationships with time-frequency representations such as the Wigner distribution, the ambiguity function, the short-time Fourier transform and the spectrogram. These relationships have a very simple and natural form and support the FRFT's interpretation as a rotation operator. Examples of FRFTs of some simple signals are given. An example of the application of the FRFT is also given