Subband- and Wavelet-Based Coding - Digital Signal Processing: Fundamentals and Applications - page 679

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FIGURE 13.56

A piecewise function in Problem 13.18.

b. Use scaling functions and wavelets fð 2 t kÞ and jð 2 t kÞ .
c. Use scaling functions and wavelets fðtÞ , jð 2 t kÞ , and jðt kÞ .
13.19. Use the Haar wavelet family to expand the signal

xðtÞ¼ sin ð 2 ptÞ for 0 t 1

a. Use only scaling functions fð 2 t kÞ .
b. Use scaling functions and wavelets fðtÞ and jðt kÞ .
13.20. Use the Haar wavelet family to expand the signal
x t ¼ e 5 t for 0 t 1

a. Use only scaling functions fð 2 t kÞ .
b. Use scaling functions and wavelets fðtÞ and jðt kÞ .

13.21. Verify the following equations using the Haar wavelet families:
a. fð 2 tÞ¼ P k ¼ N

p h 0 ðkÞfð 4 t kÞ

b. jð 2 tÞ¼ P k ¼ N

p h 1 ðkÞfð 4 t kÞ