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

Wavelet Toolbox

Example 4: Colored AR(3) Noise

Analyzing wavelet: db3

Decomposition levels: 5

Note AR(3) means AutoRegressive model of order 3.

This figure can be examined in view of the Figure 4-2,, since we are confronted here with a non-white noise whose spectrum is mainly at the higher frequencies. Therefore, it is found primarily in D₁, which contains the major portion of the signal. In this situation, which is commonly encountered in practice, the effects of the noise on the analysis decrease considerably more rapidly than in the case of white noise. In A₃, A₄ and A₅, we encounter the same scheme as that in the analysis of (see the table in Example 3: Uniform White Noise), the noise from which is built using linear filtering.

Figure 4-3: Colored AR(3) Noise

Example 4: Colored AR(3) Noise

Addressed topics

Processing noise.

The relative importance of different details.

The relative importance of D₁ and A₁.

Further exploration

Compare the detail frequencies with those in the approximations.

Compare approximations A₃, A₄, and A₅ with those shown in Figure 4-2,.

Replace AR(3) with an ARMA (AutoRegressive Moving Average) model noise. For instance:

Study an ARIMA (Integrated ARMA) model noise. For instance:

Check that each detail can be modeled by an ARMA process.

	Example 4: Colored AR(3) Noise
Addressed topics	Processing noise. The relative importance of different details. The relative importance of D₁ and A₁.
Further exploration	Compare the detail frequencies with those in the approximations. Compare approximations A₃, A₄, and A₅ with those shown in Figure 4-2,. Replace AR(3) with an ARMA (AutoRegressive Moving Average) model noise. For instance: Study an ARIMA (Integrated ARMA) model noise. For instance: Check that each detail can be modeled by an ARMA process.

Example 3: Uniform White Noise Example 5: Polynomial + White Noise