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B-Spline based Continous Wavelet Transform
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Be patient to load the applet!
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bullet References

[1] R. Ertle, Arrate Munoz, "B-spline based Continous Wavelet Transform" (EPFL-BIG-IOA Doctoral School Project)

[2] M. Unser," Splines : a perfect fit for signal and image processing ," IEEE Signal Processing Magazine, vol. 16, no. 6, pp. 22-38, November 1999.

[3] Arrate Munoz, Thierry Blu and Michael Unser, "Least-Squares Image Resizing using Finite Differences" Submitted to IEEE Transactions on Image Processing

[4] Michael Unser, Akram Aldroubi and Steven J. Schiff, "Fast Implementation of the Continous Wavelet Transform with Integer Scales" IEEE Transactions on Signal Processing, vol. 42, no. 12, pp. 3519-3523, December 1994

[5] Michael Unser "Fast Gabor-Like Windowed Fourier and Continous Wavelet Transform" IEEE Signal Processing Letters, vol. 1, no. 5, pp. 76-79, May 1994

Instruction to use the applet

  1. Define the mother wavelet you want to use : choose its B-Spline order and the number of points of its B-Spline description.
  2. Define the minimum scale and the scale-step. The CWT is computed over 256 uniformly dispersed scales.
  3. Choose wether you want to compute a real or a complex (Gabor like) CWT. In case you choose a complex CWT, the choice 'number of points' is irrelevant, and you can define the frequency of the modulating exponential.
  4. Choose the input signal you want to analyze
  5. Press the 'Run CWT' button. During computations, the 'Running' message is displayed. Once computations are done, the 'Ready' message is displayed.

The computation consists in 256 cwt's carried on a 256-samples signal. In case of a complex CWT, 2 transforms are carried respectively on the real and on the imaginary part of the modulated signal .. Be patient, it may take several seconds, depending on the power of your computer!

EPFL Swiss Federal Institute of Technology Lausanne
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21 June 2000