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过采样广泛应用于实际数字信号处理过程中。随着分数阶Fourier变换在信号处理领域的不断发展和应用,研究分数阶Fourier域过采样理论就显得十分必要.文中深入研究了分数阶Fourier域的过采样理论:导出了过采样序列与其子序列的分数阶Fourier谱关系;然后利用此关系得到了过采样序列子序列准确重建丢失采样点的表达式.最后以chirp信号为例,利用分数阶Fourier域过采样理论,证明了对于时频分布在分数阶Fourier域具有最小支撑宽度的信号,对其过采样重建更适合在分数阶Fourier域进行。
Oversampling is widely used in actual digital signal processing. With the continuous development and application of fractional Fourier transform in the field of signal processing, it is necessary to study the theory of fractional Fourier domain oversampling.In this paper, the over-sampling theory of fractional Fourier domain is studied deeply: the over-sampling sequence and its sub-sequence Then using this relationship we get the exact reconstruction of the missing sample points of the oversampled sequence subsequence.Finally, taking the chirp signal as an example, we use the fractional Fourier domain oversampling theory to prove that for the time-frequency distribution in Fractional Fourier domain The signal with the smallest support width is more suitable for over-sampling reconstruction in fractional Fourier domain.