# Detecting a Discontinuity Using a Wavelet Scalogram

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The continuous wavelet transform decomposes a signal into a series of time-varying coefficients. The wavelet scalogram plots the magnitude of these coefficients by representing each coefficient as a single row. The scalogram is a time-varying spectral representation of the signal.

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Contributed by: Olexandr Eugene Prokopchenko (October 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Wavelet transforms are excellent for identifying local discontinuities. Detection of discontinuities is valuable in signal and image processing, physics, geophysics, economics, and medicine.

References

[1] M. Bozzini, F. De Tisi, and M. Rossini, "Irregularity Detection from Noisy Data with Wavelets," *Wavelets, Images, and Surface Fitting*, Wellesley, MA: A. K. Peters, 1994 pp. 59–66.

[2] J. Canny, "A Computational Approach to Edge Detection," *IEEE Transaction on Pattern Analysis and Machine Intelligence*, 1986, pp. 8679–698.

[3] D. Lee, "Coping with Discontinuities in Computer Vision: Their Detection, Classification and Measurement," *IEEE Transaction on Pattern Analysis and Machine Intelligence*, 12, 1990 pp. 321–344.

[4] T. Gutzmer and A. Iske, "Detection of Discontinuities in Scattered Data Approximation," *Numerical Algorithms*, 16, 1997 pp. 155–170.

[5] S. Mallat and W. L. Hwang, "Singularity Detection and Processing with Wavelets," *IEEE Transactions on Information Theory*, 38(2), 1992 pp. 617–639.

## Permanent Citation

"Detecting a Discontinuity Using a Wavelet Scalogram"

http://demonstrations.wolfram.com/DetectingADiscontinuityUsingAWaveletScalogram/

Wolfram Demonstrations Project

Published: October 29 2012