Rapid update of discrete Fourier transform for real-time signal processing

Barry G. Sherlock; Yogendra P. Kakad

doi:10.1117/12.445398

22 October 2001 Rapid update of discrete Fourier transform for real-time signal processing

Proceedings Volume 4379, Automatic Target Recognition XI; (2001) https://doi.org/10.1117/12.445398
Event: Aerospace/Defense Sensing, Simulation, and Controls, 2001, Orlando, FL, United States

Abstract

In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log₂ N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log₂ N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.

Citation Download Citation

Barry G. Sherlock and Yogendra P. Kakad "Rapid update of discrete Fourier transform for real-time signal processing", Proc. SPIE 4379, Automatic Target Recognition XI, (22 October 2001); https://doi.org/10.1117/12.445398

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