COPYRIGHT 2008, PRINCETON UNIVERSITY PRESS

288 chapter 113. Reproduce the scale–time diagram shown on the right in Figure 11.10. Thisdiagram shows the output at different scales and serves to interpret the maincomponents of the signal and the time in which they appear. The time line atthe bottom of the figure corresponds to a signal of length 1 over which 256samples were recorded. The low-band (smooth) components are shown onthe left, and the high-band components on the right.a. The bottommost figure results when nend = 256.b. The figure in the second row up results from nend = 128, and we havethe output from two filterings. The output contains 256 coefficients butdivides time into four intervals and shows the frequency components ofthe original signal in more detail.c. Continue with the subdivisions for nend =64, 32, 16, 8, and 4.4. For each of these choices except the topmost, divide the time by 2 and separatethe intervals by vertical lines.5. The topmost spectrum is your final output. Can you see any relation betweenit and the chirp signal?6. Change the sign of sign and check that the inverse DWT reproduces theoriginal signal.7. Use the code to visualize the time dependence of the Daubechies motherfunction at different scales.a. Start by performing an inverse transformation on the eight-componentsignal [0,0,0,0,1,0,0,0]. This should yield a function with a width of about5 units.b. Next perform an inverse transformation on a unit vector with N =32butwith all components except the fifth equal to zero. The width should nowbe about 25 units, a larger scale but still covering the same time interval.c. Continue this procedure until you obtain wavelets of 800 units.d. Finally, with N = 1024, select a portion of the mother wavelet with data inthe horizontal interval [590,800]. This should show self-similarity similarto that at the bottom of Figure 11.11.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 288