Issue No.02 - March/April (2006 vol.8)
Denis Donnelly , Siena College
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/MCSE.2006.33
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.
fast Fourier transform, FFT, IFFT, DFT, statioinarity, linearity
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