| Fractional Fourier domain analysis of decimation and interpolation |
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| 作者单位： | MENG XiangYi（Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China） ;TAO Ran （Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China） ;WANG Yue（Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China） ; |
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| 基金项目： | 国家自然科学基金;国家自然科学基金 |
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| 摘 要： | The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital fre- quency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sam- pling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.
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| 收稿时间： | 2006-05-16 |
| 修稿时间： | 2007-05-10 |
Fractional Fourier domain analysis of decimation and interpolation |
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| Meng XiangYi,Tao Ran,Wang Yue. Fractional Fourier domain analysis of decimation and interpolation[J]. Science in China(Information Sciences), 2007, 50(4): 521-538. DOI: 10.1007/s11432-007-0040-7 |
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| Authors: | Meng XiangYi Tao Ran Wang Yue |
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| Affiliation: | Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal. Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security. Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital fre- quency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sam- pling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations. |
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| Keywords: | decimation interpolation fractional Fourier transform sampling rate conversion the digital frequency in the fractional Fourier domain |
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