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The Fast Fourier Transform for Experimentalists, Part VI: Chirp of a Bat
March/April 2006 (vol. 8 no. 2)
pp. 72-78
Denis Donnelly, Siena College
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 and Engineering, vol. 8, no. 2, pp. 72-78, March-April 2006, doi:10.1109/MCSE.2006.33
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