Example 13: A Triangle + A Sine + Noise :: Wavelets in Action: Examples and Case Studies (Wavelet Toolbox)

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Example 13: A Triangle + A Sine + Noise

Noise Analyzing wavelet: db5

Decomposition levels: 7

The signal examined here is the same as the previous signal plus a uniform white noise divided by 3. The analysis can, therefore, be compared to the previous analysis. All differences are due to the presence of the noise.

D₁ and D₂ are due to the noise.

D₃ and especially D₄ are due to the sine.

The higher level details are increasingly low, and originate in the noise.

A₇ contains a triangle, although it is not as well reconstructed as in the previous example.

Example 13: A Triangle + A Sine + Noise

Addressed topics

Detecting long-term evolution

Splitting signal components

Further exploration

Increase the amplitude of the noise.

Replace the triangle by a polynomial.

Replace the white noise by an ARMA noise.

Example 13: A Triangle + A Sine + Noise
Addressed topics	Detecting long-term evolution Splitting signal components
Further exploration	Increase the amplitude of the noise. Replace the triangle by a polynomial. Replace the white noise by an ARMA noise.

Example 12: A Triangle + A Sine Example 14: A Real Electricity Consumption Signal