Question

In this problem, we will study the filter banks that are based on the DCT. Use Eq. (6.41a) to implement a $M$-point DCT of $x(n)$ given in Figure 6.31. Assume $M=8$. a. Give the plots of $|X(k)|$. b. Also plot the frequency response of the second and third channel analysis filters that are associated with the basis vectors $h_1(n)$ and $h_2(n)$. c. Plot the impulse response of $h_1(n)$ and see if it is symmetric. d. Is the DCT filter bank evenly stacked or oddly stacked?

   In this problem, we will study the filter banks that are based on the DCT. Use Eq. (6.41a) to implement a $M$-point DCT of $x(n)$ given in Figure 6.31. Assume $M=8$.
a. Give the plots of $|X(k)|$.
b. Also plot the frequency response of the second and third channel analysis filters that are associated with the basis vectors $h_1(n)$ and $h_2(n)$.
c. Plot the impulse response of $h_1(n)$ and see if it is symmetric.
d. Is the DCT filter bank evenly stacked or oddly stacked?

Audio Signal Processing and Coding

Andreas Spanias, Ted… 1st Edition

Chapter 6, Problem 13

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We need to perform the following tasks: - Compute the DCT of a given signal $ x(n) $ with $ M = 8 $. - Plot the magnitude of the DCT coefficients $ |X(k)| $. - Plot the frequency response of the second and third channel analysis filters. - Plot the impulse Show more…

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In this problem, we will study the filter banks that are based on the DCT. Use Eq. (6.41a) to implement a $M$-point DCT of $x(n)$ given in Figure 6.31. Assume $M=8$. a. Give the plots of $|X(k)|$. b. Also plot the frequency response of the second and third channel analysis filters that are associated with the basis vectors $h_1(n)$ and $h_2(n)$. c. Plot the impulse response of $h_1(n)$ and see if it is symmetric. d. Is the DCT filter bank evenly stacked or oddly stacked?

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