Detecting a Discontinuity Using a Wavelet Scalogram
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.
In the upper plot, a removable (point) and jump discontinuity for the sine function is shown. In the lower plot, the wavelet scalogram is shown. The lower-order coefficients give information about the high frequency components in the signal and are therefore able to capture the presence of any abrupt changes in the signal. The location of discontinuities in signals can therefore be captured well using wavelet analysis, as shown in the wavelet scalogram.