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Fast Gabor-Like Windowed Fourier and Continuous Wavelet Transforms

M. Unser

IEEE Signal Processing Letters, vol. 1, no. 5, pp. 76-79, May 1994.



Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by convolving a premodulated signal with a Gaussian-like window and demodulating the output. The window functions are either B-splines dilated by an integer factor m or quasi-Gaussians of arbitrary size generated from the n-fold convolution of a symmetrical exponential. Both approaches result in a recursive implementation with a complexity independent of the window size (O(N)).

Erratum

  • p. 77, the right-hand side of Equation (14) should read (2 α) ⁄ (1 - α)2 instead of α2 ⁄ (1 - α)2.


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AUTHOR="Unser, M.",
TITLE="Fast {G}abor-Like Windowed {F}ourier and Continuous Wavelet
        Transforms",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="1994",
volume="1",
number="5",
pages="76--79",
month="May",
note="")

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