Wavelets in Action: Examples and Case Studies (Wavelet Toolbox)

Wavelet Toolbox

Example 12: A Triangle + A Sine

Analyzing wavelet: db5

Decomposition levels: 6

The signal is the sum of a sine having a period of approximately 20 and of a "triangle".

D₁ and D₂ are very small. This suggests that the signal contains no components with periods that are short in relation to the sampling period.

D₃ and especially D₄ can be attributed to the sine. The jump of the sine from A₃ to D₄ is clearly visible.

The details for the higher levels D₅ and D₆ are small, especially D₅.

D₆ exhibits some edge effects.

A₆ contains the triangle which includes only low frequencies.

Figure 4-11: A Triangle + A Sine

Example 12: A Triangle + A Sine

Addressed topics

Detecting long-term evolution.

Splitting signal components.

Identifying the frequency of a sine.

Further exploration

Try using sinusoids whose period is a power of 2.

	Example 12: A Triangle + A Sine
Addressed topics	Detecting long-term evolution. Splitting signal components. Identifying the frequency of a sine.
Further exploration	Try using sinusoids whose period is a power of 2.

Example 11: A Sine + White Noise Example 13: A Triangle + A Sine + Noise