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Issue No.02 - March/April (2006 vol.8)
pp: 72-78
Denis Donnelly , Siena College
ABSTRACT
Two assumptions underlie the Fourier transform process: stationarity and linearity. When signals deviate from these conditions, the transform outcomes are suspect. A chirp, which by definition has a frequency that varies with time, doesn't satisfy these requirements, and its fast Fourier transform (FFT) doesn't adequately express the changing nature of the signal's frequency content. In this analysis of a bat chirp, I first examine how the FFT handles a chirp and then how we can use a sequence of windows that individually span only a portion of the total time-domain signal to generate a frequency versus time description of the signal. The trade-off in this kind of windowing is between dynamic response and resolution: we obtain improved dynamics if we use shorter windows, whereas we get better resolution with longer windows. I conclude this article and this series with a brief look at the Hilbert-Huang transform, which isn't constrained by the same assumptions as the FFT.
INDEX TERMS
fast Fourier transform, FFT, IFFT, DFT, statioinarity, linearity
CITATION
Denis Donnelly, "The Fast Fourier Transform for Experimentalists, Part VI: Chirp of a Bat", Computing in Science & Engineering, vol.8, no. 2, pp. 72-78, March/April 2006, doi:10.1109/MCSE.2006.33