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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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