Wavelet Toolbox

Suppressing Signals

The purpose of this example is to illustrate the property that causes the decomposition of a polynomial to produce null details, provided the number of vanishing moments of the wavelet (N for a Daubechies wavelet dbN) exceeds the degree of the polynomial. The signal here is a second-degree polynomial combined with a small amount of white noise.

Note that only the noise comes through in the details. The peak-to-peak magnitude of the details is about 2, while the amplitude of the polynomial signal is on the order of 10⁵.

The db3 wavelet, which has three vanishing moments, was used for this analysis. Note that a wavelet of the Daubechies family with fewer vanishing moments would fail to suppress the polynomial signal. For more information, see the section Daubechies Wavelets: dbN.

Here is what the first three details look like when we perform the same analysis with db2.

The peak-to-peak magnitudes of the details D1, D2, and D3 are 2, 10, and 40, respectively. These are much higher detail magnitudes than those obtained using db3.

Discussion

Discussion