Fast Interpolation Algorithms for Signals in One and Two Dimensions
Nuaa Nanjing · Nanjing Hangkong Hangtian Daxue xuebao · 1995
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.