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The paper reveals the relationship between the weighting coefficients and weighted functions via the research of coefficients matrix and based on the original definition of 4-weighted fractional Fourier transform(4-WFRFT).The multi-parameters expression of weighting coefficients are given.Moreover, the 4-WFRFT of discrete sequences is defined by introducing DFT into it, which makes it suitable for digital communication systems.After analyzing the properties of WFRFT, a typical scheme for modulation/demodulation is proposed, which could make the statistics properties of the real and image part on both of the time and frequency domain and the phase properties have a significant variation.Such a variation could be controlled by the adjustment of transform parameters.If the WFRFT of multi-parameters is implemented, it will be more difficult to intercept and capture the modulated signals than normal.
The paper reveals the relationship between the weighting coefficients and weighted functions via the research of coefficient matrix and based on the original definition of 4-weighted fractional Fourier transform (4-WFRFT). The multi-parameters expression of weighting coefficients are given. Moreover, the 4-WFRFT of discrete sequences is defined by introducing DFT into it, which makes it suitable for digital communication systems .After analyzing the properties of WFRFT, a typical scheme for modulation / demodulation is proposed, which could make the statistics properties of the real and image part on both of the time and frequency domain and the phase properties have a significant variation. Controllable could be controlled by the adjustment of transform parameters. IF the WFRFT of multi-parameters is implemented, it will be more difficult to intercept and capture the modulated signals than normal.