Fast Gabor-like windowed Fourier and continuous wavelet transforms
- 1 May 1994
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Signal Processing Letters
- Vol. 1 (5) , 76-79
- https://doi.org/10.1109/97.294384
Abstract
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)).Keywords
This publication has 15 references indexed in Scilit:
- An efficient recursive algorithm for time-varying Fourier transformIEEE Transactions on Signal Processing, 1993
- B-spline signal processing. II. Efficiency design and applicationsIEEE Transactions on Signal Processing, 1993
- The discrete wavelet transform: wedding the a trous and Mallat algorithmsIEEE Transactions on Signal Processing, 1992
- On the asymptotic convergence of B-spline wavelets to Gabor functionsIEEE Transactions on Information Theory, 1992
- Fast algorithms for discrete and continuous wavelet transformsIEEE Transactions on Information Theory, 1992
- Recursive regularization filters: design, properties, and applicationsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1991
- The wavelet transform, time-frequency localization and signal analysisIEEE Transactions on Information Theory, 1990
- Some Aspects of Non-Stationary Signal Processing with Emphasis on Time-Frequency and Time-Scale MethodsPublished by Springer Nature ,1989
- Comments, with reply, on 'A new approach to recursive Fourier transform'Proceedings of the IEEE, 1988
- Decomposition of Hardy Functions into Square Integrable Wavelets of Constant ShapeSIAM Journal on Mathematical Analysis, 1984