Improving the accuracy and error analysis in floating‐point FFT computation

Abstract

The cause of the error in the FFT is due mostly to the quantization error of the input data, the round‐off error in arithmetic operation, and the computation error of Wnk= exp (‐j 2nk /N). of these, the error of Wnk is complex, and this error is approximated in the reported error analysis by the truncation error by finite bits. This paper examines the actual computation error of Wnk and its effect. As a result, it is shown that the computation error of Wnk is much larger than the truncation error by the finite bits, and can produce instability in the algorithm. Then to solve the problem, this paper proposes a method to improve the computation accuracy of Wnk. the proposed method can be executed without increasing greatly the processing time and the memory, compared with the direct FFT computation. By using the proposed processing, the error analysis is made more reliable than in the past and the error accompanying the FFT is reduced. Finally, the effectiveness of the proposed method is verified by several examples.