Angular decompositions for the discrete fractional signal transforms
Signal Processing
Signal Processing - Special section: Advances in signal processing-assisted cross-layer designs
Sliding discrete fractional transforms
Signal Processing
Sampling rate conversion for linear canonical transform
Signal Processing
Sampling and discretization of the linear canonical transform
Signal Processing
Time-delay estimation of chirp signals in the fractional Fourier domain
IEEE Transactions on Signal Processing
Using fractional Fourier transform in time-frequency analysis for bird songs
SPPRA '08 Proceedings of the Fifth IASTED International Conference on Signal Processing, Pattern Recognition and Applications
Short-time fractional fourier transform and its applications
IEEE Transactions on Signal Processing
MIMO OFDM Systems Based on the Optimal Fractional Fourier Transform
Wireless Personal Communications: An International Journal
ICI analysis for FRFT-OFDM systems to frequency offset in time-frequency selective fading channels
IEEE Communications Letters
Image encryption with multiorders of fractional Fourier transforms
IEEE Transactions on Information Forensics and Security
Fractional Fourier transform: a survey
Proceedings of the International Conference on Advances in Computing, Communications and Informatics
Multi-channel filter banks associated with linear canonical transform
Signal Processing
Biorthogonal Frequency Division Multiple Access Cellular System with Angle Division Reuse Scheme
Wireless Personal Communications: An International Journal
Doppler Estimation from Echo Signal Using FRFT
Wireless Personal Communications: An International Journal
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The discrete fractional Fourier transform (DFRFT) is the generalization of discrete Fourier transform. Many types of DFRFT have been derived and are useful for signal processing applications. We introduce a new type of DFRFT, which are unitary, reversible, and flexible; in addition, the closed-form analytic expression can be obtained. It works in performance similar to the continuous fractional Fourier transform (FRFT) and can be efficiently calculated by the FFT. Since the continuous FRFT can be generalized into the continuous affine Fourier transform (AFT) (the so-called canonical transform), we also extend the DFRFT into the discrete affine Fourier transform (DAFT). We derive two types of the DFRFT and DAFT. Type 1 is similar to the continuous FRFT and AFT and can be used for computing the continuous FRFT and AFT. Type 2 is the improved form of type 1 and can be used for other applications of digital signal processing. Meanwhile, many important properties continuous FRFT and AFT are kept in the closed-form DFRFT and DAFT, and some applications, such as filter design and pattern recognition, are also discussed. The closed-form DFRFT we introduce has the lowest complexity among all current DFRFTs that is still similar to the continuous FRFT