Wavelet Toolbox

Example 14: A Real Electricity Consumption Signal

Analyzing wavelet: db3

Decomposition levels: 5

The series presents a peak in the center, followed by two drops, a shallow drop, and then a considerably weaker peak.

The details for levels 1 and 2 are of the same order of magnitude and give a good expression of the local irregularities caused by the noise. The detail for level 3 presents high values in the beginning and at the end of the main peak, thus allowing us to locate the corresponding drops. The detail D₄ shows coarser morphological aspects for the series (i.e., three successive peaks). This fits the shape of the curve remarkably well, and includes the essential signal components for periods of less than 32 time-units. The approximations show this effect clearly: A₁ and A₂ bear a strong resemblance; A₃ forms a reasonably accurate approximation of the original signal. A look at A₄, however, shows that a considerable amount of information has been lost.

In this case, as a conclusion, the multiscale aspect is the most interesting and the most significant feature: the essential components of the electrical signal used to complete the description at 32 time-units (homogeneous to A₅) are the components with a period between 8 and 16 time-units.

Example 14: A Real Electricity Consumption Signal
Addressed topics	Detecting long-term evolution Splitting signal components Detecting breakdown points Multiscale analysis
Further exploration	Try the same analysis on various sections of the signal. Focus on a range other than the [3600:3700] shown here.

This signal is explored in much greater detail in Case Study: An Electrical Signal.

Example 13: A Triangle + A Sine + Noise

Case Study: An Electrical Signal

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