Wavelet Toolbox

Illustrated Examples

Fourteen illustrated examples are included in this section, organized as shown:

Example	Equation	Signal Name	MAT-File
Example 1: A Sum of Sines	A sum of sines:	s1(t)	sumsin
Example 2: A Frequency Breakdown	A frequency breakdown:	s2(t)	freqbrk
Example 3: Uniform White Noise	A uniform white noise: on the interval	b1(t)	whitnois
Example 4: Colored AR(3) Noise	A colored AR(3) noise :	b2(t)	warma
Example 5: Polynomial + White Noise	A polynomial + a white noise: on the interval	s3(t)	noispol
Example 6: A Step Signal	A step signal:	s4(t)	wstep
Example 7: Two Proximal Discontinuities	Two proximal discontinuities:	s5(t)	nearbrk
Example 8: A Second-Derivative Discontinuity	A second-derivative discontinuity: s6 is f3 sampled at 10-3	s6(t)	scddvbrk
Example 9: A Ramp + White Noise	A ramp + a white noise:	s7(t)	wnoislop
Example 10: A Ramp + Colored Noise	A ramp + a colored noise:	s8(t)	cnoislop
Example 11: A Sine + White Noise	A sine + a white noise:	s9(t)	noissin
Example 12: A Triangle + A Sine	A triangle + a sine:	s10(t)	trsin
Example 13: A Triangle + A Sine + Noise	A triangle + a sine + a noise:	s11(t)	wntrsin
Example 14: A Real Electricity Consumption Signal	A real electricity consumption signal	--	leleccum

Please note that

• All the decompositions use Daubechies wavelets.
• The examples show the signal, the approximations, and the details.

The examples include specific comments and feature distinct domains -- for instance, if the level of decomposition is 5,

• The left column contains the signal and the approximations A₅ to A₁.
• The right column contains the signal and the details D₅ to D₁.
• The approximation A₁ is located under A₂, A₂ under A₃, and so on; the same is true for the details.
• The abscissa axis represents the time; the unit for the ordinate axis for approximations and details is the same as that of the signal.
• When the approximations do not provide enough information, they are replaced by details obtained by changing wavelets.
• The examples include questions for you to think about:
• What can be seen on the figure?
• What additional questions can be studied?

Wavelets in Action: Examples and Case Studies

Advice to the Reader