Wavelet Toolbox

Illustrated Examples

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

Example	Figure	Page	Description of the Signal	Signal Name	MAT-file
1	4-1	4-10	A sum of sines:	s1(t)	sumsin
2	4-1	4-12	A frequency breakdown:	s2(t)	freqbrk
3	4-2	4-13	A uniform white noise: on the interval	b1(t)	whitnois
4	4-3	4-16	A colored AR(3) noise	b2(t)	warma
5	4-4	4-19	A polynomial + a white noise: on the interval	s3(t)	noispol
6	4-5	4-21	A step signal:	s4(t)	wstep
7	4-6	4-23	Two proximal discontinuities:	s5(t)	nearbrk
8	4-7	4-25	A second-derivative discontinuity: s6 is f3 sampled at 10-3	s6(t)	scddvbrk
9	4-8	4-27	A ramp + a white noise:	s7(t)	wnoislop
10	4-9	4-29	A ramp + a colored noise:	s8(t)	cnoislop
11	4-10	4-31	A sine + a white noise:	s9(t)	noissin
12	4-11	4-33	A triangle + a sine:	s10(t)	trsin
13	4-12	4-35	A triangle + a sine + a noise:	s11(t)	wntrsin
14	4-13	4-37	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