抽样率转换的分数阶Fourier域分析

Analysis of Sampling-Rate Conversion in the Fractional Fourier Domain

为了节省计算量及存储空间,在一个信号处理系统中常常需要不同的抽样率及其相互之间的转换.而在分数阶Fourier域中分析信号完全可用较低的抽样频率来抽样(低于Nyquist抽样率),这就意味着建立在频域上的传统抽样率转换理论将不再适用.本文将建立在Fourier变换(频域)上的传统抽样率转换理论推广到了分数阶Fourier域,通过研究时域抽取和零值内插操作在分数阶Fourier域的表示及其含义,导出了基于分数阶Fourier变换的有理分数倍抽样率转换理论.可以看到,将分数阶Fourier变换的变换阶数取为π/2,便得到了与传统频域多抽样率理论完全一致的结果.最后,本文通过仿真对导出的分数阶Fourier域多抽样率理论进行了验证.

In order to decrease the computation and storage load, different sampling-rates, together with the Sampling-rate Conversion,are often used in a system.When a signal is analyzed in the fractional Fourier domain,the lower sampling-rate could be adopted than the Nyquist sampling-rate, which means that the traditional sampling-rate conversion theory, founded in the frequency domain,could be disabled under the circumstances. The traditional sampling-rate conversion theory is generalized to obtain the version for the fractional Fourier transform （FRFT） .First,the formulas and signification of decimation and interpolation are studied in the fractional Fourier domain. Based on these results, the sampling-rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced. It＇s obvious that the sampling-rate conversion theory for the FRFT changes to the traditional version when the FRFT order equals π/2. Finally, the theory obtained in this paper is verified by some simulations.