Question

n this problem, we will study the filter banks that are based on the DFT. Use Eq. (6.39a) to implement a $2 M$-point DFT of $x(n)$ given in Figure 6.31. Assume $M=8$. a. Give the plots of $|X(k)|$. b. 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. State whether the DFT filter bank is evenly stacked or oddly stacked.

   n this problem, we will study the filter banks that are based on the DFT. Use Eq. (6.39a) to implement a $2 M$-point DFT of $x(n)$ given in Figure 6.31. Assume $M=8$.
a. Give the plots of $|X(k)|$.
b. 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. State whether the DFT filter bank is evenly stacked or oddly stacked.

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Audio Signal Processing and Coding

Audio Signal Processing and Coding

Andreas Spanias, Ted… 1st Edition

Chapter 6, Problem 12

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Step 1

(6.39a) with $M=8$. - Calculate the DFT using the formula: $X(k) = \sum_{n=0}^{2M-1} x(n) e^{-j2\pi kn/(2M)}$ - Substitute $M=8$ and calculate $X(k)$ for $k=0,1,...,15$. Show more…

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n this problem, we will study the filter banks that are based on the DFT. Use Eq. (6.39a) to implement a $2 M$-point DFT of $x(n)$ given in Figure 6.31. Assume $M=8$. a. Give the plots of $|X(k)|$. b. 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. State whether the DFT filter bank is evenly stacked or oddly stacked.

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