一维与二维信号的快速内插算法

一维信号的快速内插在语音处理、数字波束形成、雷达实时仿真等方面有重要应用。图象处理中则常需对二维信号进行内插。文中首先提出了一种利用ＦＦＴ的一维信号内插的子序列算法。去除了Ａｄａｍｓ算法的额外补偿项ｅｒ（ｍ）与其他冗余运算，所需实乘数只有Ａｄａｍｓ算法的２０％左右，实加数约为Ａｄａｍｓ算法的３０％。然后本文又提出了一种基于子序列ＦＦＴ的二维信号快速内插算法。该算法不仅解决了Ｓａｔｈｙａｎａｒａｙａ

Fast Interpolation Algorithms for Signals in One and Two Dimensions

The fast interpolation of 1-D signals finds important applications in speech processing,digital beam forming, radar real-time simulation etc. The interpolation of 2-D signals may often be required in image processing. In this paper, a subsequence approach to the interpolation of 1-D signals using FFT is proposed. It does not need the extra compensation term er(m) as in Adams's proposal, and some unnecessary computations may be eliminated. As compared with Adams's algorithm, the number of real multiplication operations is reduced by 80% and the number of real addition operations is reduced by 70%.Then, the subsequence interpolation algorithm using FFT for 2-D signals is proposed. The algorithm ensures that the interpolated signal will be real-valued, provided that the signal to be interpolated is real-valued, but Sathyanarayana's algorithm and Mao yimin's algorithm produce interpolated signals with nonzero imaginary components. The proposed algorithm can reduce significantly the number of arithmetic operations using the complex-conjugate circular symmetry which characterizes the DFT of real-valued signals. As compared with Mao yimin's algorithm, the number of real multiplication operations is reduced by 80% and the number of real addition operations is reduced by 70%. The fast interpolation algorithms for signals in one and two dimensions permit of any integer-valued interpolation ratio and are particularly appropriate for parallel processing. They are efficient in practical signal processing.