In this problem, we will design and analyze a four-channel...

In this problem, we will design and analyze a four-channel uniform treestructured QMF bank. a. Given $H_{00}(z)=1+0.1 z^{-1}$ and $H_{10}(z)=1+0.9 z^{-1}$. Complete the tree-structured QMF bank (use Figure 6.8) for four channels. b. Using the identities given in Figure 6.10 (or Eq. (6.11)), construct a parallel analysis-synthesis filter bank. The parallel analysis-synthesis filter bank structure must be similar to the one shown in Figure 6.1 with $M=4$. c. Plot the frequency response of the resulting parallel filter bank analysis filters, i.e., $H_0(z), H_1(z), H_2(z)$, and $H_3(z)$. Comment on the pass-band and stopband structures of the magnitude responses associated with these filters. d. Plot the impulse response $h_1(n)$. Is $h_1(n)$ symmetric?

In this problem, we will design and analyze a four-channel uniform treestructured QMF bank.
a. Given $H_{00}(z)=1+0.1 z^{-1}$ and $H_{10}(z)=1+0.9 z^{-1}$. Complete the tree-structured QMF bank (use Figure 6.8) for four channels.
b. Using the identities given in Figure 6.10 (or Eq. (6.11)), construct a parallel analysis-synthesis filter bank. The parallel analysis-synthesis filter bank structure must be similar to the one shown in Figure 6.1 with $M=4$.
c. Plot the frequency response of the resulting parallel filter bank analysis filters, i.e., $H_0(z), H_1(z), H_2(z)$, and $H_3(z)$. Comment on the pass-band and stopband structures of the magnitude responses associated with these filters.
d. Plot the impulse response $h_1(n)$. Is $h_1(n)$ symmetric?

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