Wavelet Toolbox

Example 2: A Frequency Breakdown

Analyzing wavelet: db5

Decomposition levels: 5

The signal is formed of a slow sine and a medium sine, on either side of 500. These two sines are not connected in a continuous manner: D₁ and D₂ can be used to detect this discontinuity. It is localized very precisely: only a small domain around 500 contains large details. This is because the rupture contains the high-frequency part; the frequencies in the rest of the signal are not as high. It should be noted that if we are interested only in identifying the discontinuity, db1 is more useful than db5.

D₃ and D₄ contain the medium sine as in the previous analysis. The slow sine appears clearly alone in A₅. It is more regular than in the s₁ analysis, since db5 is more regular than db3. If the same signal had been analyzed by the Fourier transform, we would not have been able to detect the instant corresponding to the signal's frequency change, whereas it is clearly observable here.

Example 2: A Frequency Breakdown
Addressed topics	Suppressing signals Detecting long-term evolution
Further exploration	Compare to the signal s1. On a longer signal, select a deeper level of decomposition in such a way that the slow sinusoid appears into the details. Compare with a Fourier analysis. Compare with a windowed Fourier analysis.

Example 1: A Sum of Sines

Example 3: Uniform White Noise

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