scholarly journals Multiweighted-Type Fractional Fourier Transform: Unitarity

2021 ◽  
Vol 5 (4) ◽  
pp. 205
Author(s):  
Tieyu Zhao ◽  
Yingying Chi
Keyword(s):  
Fourier Transform ◽  
Fractional Order ◽  
Fractional Fourier Transform ◽  
Program Code ◽  
Signal Process ◽  
Discrete Fractional Fourier Transform ◽  
Growing Body ◽  
Basic Functions ◽  
Definition Of ◽  
Weighted Type

The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform as basic functions to prove and discuss the unitarity. Thanks to the growing body of research, we found that the effective weighting term of the M-WFRFT is only four terms, none of which are extended to M terms, as described in the definition. Furthermore, the program code is analyzed, and the result shows that the previous work (Digit Signal Process 2020: 104: 18) based on MATLAB for unitary verification is inaccurate.

scholarly journals Three Term Weighted Type Fractional Fourier Transform Based Generalized Hybrid Carrier and Its Application into PAPR Suppression

2021 ◽  
Author(s):  
Yong Li ◽  
Zhiqun Song ◽  
Teng Sun ◽  
Bin Wang
Keyword(s):  
Fourier Transform ◽  
Orthogonal Frequency Division Multiplexing ◽  
Fractional Fourier Transform ◽  
Average Power ◽  
The Novel ◽  
Cumulative Density Function ◽  
Ofdm System ◽  
Single Carrier ◽  
Definition Of ◽  
Weighted Type

To suppress the peak to average power ratio (PAPR) of wireless communication based upon multi-carrier system. We, in this paper, proposed the three term weighted type fractional Fourier transform (3-WFRFT) based generalized hybrid carrier (GHC) system. We first provide the definition of 3-WFRFT. Moreover, some useful properties of 3-WFRFT have been presented, in this paper, which will helpful to comprehend the novel 3-WFRFT transform. Furthermore, we take PAPR of the proposed algorithm, in comparison with orthogonal frequency division multiplexing (OFDM) system and single carrier modulation (SC) system under typical complementary cumulative density function (CCDF) level. It would be demonstrated that, from some numerical simulations, the proposed 3-WFRFT based GHC performs better than OFDM system and will be useful to reduce the PAPR level.

Sliding 2D Discrete Fractional Fourier Transform

2019 ◽  
Vol 26 (12) ◽  
pp. 1733-1737 ◽  
Author(s):  
Yu Liu ◽  
Hongxia Miao ◽  
Feng Zhang ◽  
Ran Tao
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Discrete Fractional Fourier Transform
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