Q3) [15 pts] Assume that you have a signal s = (s(1), s(2), ..s(n)). Let us...

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Q3) [15 pts] Assume that you have a signal s = (s(1), s(2), ..s(n)). Let us represent its DCT transform as t = (t(1), t(2), ...(n)). Suppose you remove 25% of coefficients in t, set them to 0's. The result is tt =(t(1), t(2), (k), 0, 0, 0, ...0) where k = 0.75*n. Use this information to answer the following Questions (A and B). %3D A) [3 pts] Let (d1) be the distortion in transform domain. Write down the expression for (d1) in terms of t's. B) [3 pts] Let us reconstruct the signal by applying the inverse transform on tt. Let us say, the output is ss. Suppose you compute the mean square error (d2) between s and ss. Is d2 = d1? Why? C) [3 pts] Is DCT better than KLT? Why? D) [3 pts] Is DWT better than DCT? Why? Q3) [15 pts] Assume that you have a signal s = (s(1), s(2), ..s(n)). Let us represent its DCT transform as t = (t(1), t(2), ...(n)). Suppose you remove 25% of coefficients in t, set them to 0's. The result is tt =(t(1), t(2), (k), 0, 0, 0, ...0) where k = 0.75*n. Use this information to answer the following Questions (A and B). %3D A) [3 pts] Let (d1) be the distortion in transform domain. Write down the expression for (d1) in terms of t's. B) [3 pts] Let us reconstruct the signal by applying the inverse transform on tt. Let us say, the output is ss. Suppose you compute the mean square error (d2) between s and ss. Is d2 = d1? Why? C) [3 pts] Is DCT better than KLT? Why? D) [3 pts] Is DWT better than DCT? Why?

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