In this problem, we will study the filter banks based on the...

In this problem, we will study the filter banks based on the MDCT. a. First, design a sine window, $w(n)=\sin [(2 n+1) \pi / 4 M]$ with $M=8$. b. Check if the sine window satisfies the generalized perfect reconstruction conditions, i.e., Eqs. (6.28a) (6.28b). c. Next, design a MDCT analysis filter bank, $h_k(n)$, for $0<k<7$. Figure 6.31. Input signal, $x(n)$, for Problems 6.12, 6.13, and 6.14. FIGURE CANT COPY d. Plot both the impulse response and the frequency response of the analysis filters, $h_1(n)$ and $h_2(n)$. e. Compute the MDCT coefficients, $X(k)$, of the input signal, $x(n)$, shown in Figure 6.31. f. Is the impulse response of the analysis filter, $h_1(n)$, symmetric?

In this problem, we will study the filter banks based on the MDCT.
a. First, design a sine window, $w(n)=\sin [(2 n+1) \pi / 4 M]$ with $M=8$.
b. Check if the sine window satisfies the generalized perfect reconstruction conditions, i.e., Eqs. (6.28a) (6.28b).
c. Next, design a MDCT analysis filter bank, $h_k(n)$, for $0<k<7$.
Figure 6.31. Input signal, $x(n)$, for Problems 6.12, 6.13, and 6.14.
FIGURE CANT COPY
d. Plot both the impulse response and the frequency response of the analysis filters, $h_1(n)$ and $h_2(n)$.
e. Compute the MDCT coefficients, $X(k)$, of the input signal, $x(n)$, shown in Figure 6.31.
f. Is the impulse response of the analysis filter, $h_1(n)$, symmetric?

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