Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the overs...Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.展开更多
基金Supported partially by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104)the National Natural Science Foundation of China (Grant Nos. 60890072, 60572094)the National Basic Research Program of China (Grant No.2009CB724003)
文摘Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.
