Audio Signal Processing and Coding

COMPUTER EXERCISE

8.8. Let the scaling function, ϕ(t), and the mother wavelet function, ξ(t), be as shown in Figure 8.15(a) and Figure 8.15(b), respectively. Assume that the input signal, x(t), is as shown in Figure 8.15(c). Given the wavelet series expansion,

where both υ and τ are integers and denote the dilation and translation indices, respectively, α(τ) and β(υ, τ) are the wavelet expansion coefficients. Solve for α(τ) and β(υ, τ).

[Hint: Compute the coefficients using inner products, and

Audio Signal Processing and Coding, by Andreas Spanias, Ted Painter, and Venkatraman AttiCopyright © 2007 by John Wiley & Sons, Inc.